When I played Skyrim, it was obvious to me that it was a pretty shallow, mediocre RPG with a lot of problems. I had a whole bunch of criticisms to lay against it, and I still don't understand how people consider it such a great, phenomenal game. Replaying Fallout: New Vegas made it painfully clear that Bethesda really has no idea what they're doing when it comes to implementing RPG mechanics and designing sophisticated, compelling gameplay. New Vegas is a better RPG than Skyrim, and here's why.
It matters how you choose to solve quests
In Skyrim, an overwhelming majority of quests have one single path with one single solution. Most of the time you're rail-roaded into following the game's pre-determined course with little input of your own on how things are accomplished or how they turn out. The guild quests are particularly iconic of this; they're entirely straightforward and devoid of role-playing options, forcing you to commit your soul to Hircine for all eternity to complete the Companion's guild or swear a lifetime of servitude to Nocturnal to complete the Thieves guild. You are simply a means to an end, no more sophisticated than a monkey mindlessly pushing buttons and pulling levers to make an automated contraption go forward along the tracks.
In good RPGs, two different players can face the same situation, have different thoughts or feelings on it, and come to different solutions. Even if they come to the same solution, they may devise different ways to accomplish it. This is largely what RPGs are about; having the freedom to make decisions which will have unique consequences on the course of the game, often based on how you've chosen to develop and role-play your character. With Skyrim, it doesn't matter how you've built your character or what your own unique perspective on the quest is -- it's going to have the exact same progression no matter what.
There are occasional instances in Skyrim where you have different options, where the questline actually branches off, but these are generally the exception to the rule and, for the most part, have little consequence of their own. I sided with the Stormcloaks, for example, and had a quest where we stormed Whiterun to overthrow the Jarl. At first I thought it was great, seeing a familiar environment change based on my actions that would have lasting implications on the game. But once everything was said and done, Whiterun practically reverted back to the way it was before. For all intents and purposes, it hadn't changed one bit.
In New Vegas, a far greater percentage (also contributing a greater raw number) of quests have different role-playing options and outcomes. The very first quest, for example, gives you the choice of defending Goodsprings from an attack by the local Powder Gangers, or you can ally with the Powder Gangers and attack Goodsprings. No matter which path you take, you have different prelimary options which will affect the battle itself. Once the battle has completed, the town remains permanently changed depending on your decisions and actions, while opening doors for new quests or closing doors for other quests.
This is the overall theme of questing in New Vegas; most of the time quests provide optional deviations in the path, letting you skip certain parts or go into greater detail on others or even sway the outcome of things. How you solve the quest matters, allowing each quest to unfold differently, yielding different rewards, and having lasting impact and consequences on certain characters, locations, or factions. The quests in New Vegas give you a genuine feeling of control over your character and the environment, whereas Skyrim makes you feel like a hollow vessel who has no real say in anything.
It matters what order you do things
One of the major problems with Skyrim as an RPG is that almost every bit of content is designed to be completely self-contained and isolated from everything else. Nothing conflicts or overlaps, ensuring that any character can complete any bit of content at any point in the game. Whether you go to Whiterun first, or Markarth first, or Riften first, it really doesn't matter, because events in one location won't have any effects on other locations. Consequently, there's no meaningful sense of structure or progression throughout the game.
People argue that Skyrim is a better open-world RPG, and that's technically true because Skyrim is a lot more "open" than New Vegas. You can't realistically go anywhere you want at any time in New Vegas because you're going to get killed or not meet the pre-requisites for that area, so it has more restrictions in terms of its "openness." Skyrim has a lot more open freedom than New Vegas, but that freedom is pretty shallow and worthless without consequences -- being able to go anywhere and do anything at any time makes everything feel extraneous and sort of pointless.
In New Vegas, it matters what order you visit locations and what order you complete quests, and even whether or not you do quests at all. New Vegas is just as open as Skyrim in the sense that you can go anywhere and do quests in any order at the start of the game, but it does so with direction and focus. There's obviously an intended path you're supposed to follow -- a circular route down south and then looping back around towards the north side of Vegas -- but you're always free to deviate from this path, and doing so will have different, unique effects on the game.
Almost everything in New Vegas has some kind of relation to everything else, whether it be neighboring regions or an entire faction across the Mojave. Many quests overlap, factions conflict, and most areas are tied to other areas, meaning that there are consequences for how you explore and complete content. If you visit a location without having picked up a quest elsewhere, the locals may be hostile; if you kill them in self-defense, you may prevent yourself from completing an entire sequence of quests, and might have just cost yourself an opportunity to earn valuable reputation points with a faction.
Having an intended path like that also lets the developers create side-quests that specifically compliment the main questline (rather than being completely superfluous sideshow distractions), where one action will have subsequent outcomes on later locations. The content you experience will be different based on what you do with more prominent, noticeable effects on the immediate gameplay, which makes it far more compelling to explore thoroughly and complete quests intelligently to make sure you're experiencing as much as you can and optimizing your playthrough.
It matters what stats you have
Most of the stats and perks in Skyrim have little real impact on the gameplay or your role-playing options. A majority of quests are designed to happen the same regardless of whatever stats or skills you may have (a burly warrior who's only cast a handful of novice-level spells is able to become Guild Master of the college of Winterhold), and there are scarce few opportunities to put your character's attributes to use in any avenue besides combat. For the most part, the skills and perks in Skyrim are passive modifiers that don't make an active difference in gameplay, or they're just completely pointless. Take speechcraft, for example -- the skill is conventionally meant to allow for diplomatic solutions to quests, as well as to access new areas of content, but in 130 hours of gameplay I only had maybe a half-dozen opportunities to actually persuade people.
Skyrim completely did away with base attributes like strength, dexterity, and intelligence stats that the Elder Scrolls series is known for. I always thought the leveling system in TES was flawed and counter-intuitive, so I was kind of grateful that Bethesda did away with that system, but what they put in its place (or rather, didn't) simply leaves a bit of a void of statistical RPG mechanics. The absence of stats is one less way to build and role-play a given character, when there was a lot of potential for these to have fun impacts on the gameplay. Just look at how New Vegas handles the intelligence stat, with low-intelligence characters talking like morons, and high-perception characters able to pick up on things other characters might miss.
In New Vegas, skill checks show up in dialogue and quest solutions a lot. The starting quest in Goodsprings allows you to improve the town's odds of survival in a fight against the Powder Gangers depending on how you've decided to build your barter, explosives, speech, sneak, and medicine skills. The game specifically rewards you for choosing certain perks while punishing you (or more generally, withholding rewards) for neglecting others. These skills affect your combat prowess, but they also have a huge impact on how you can ago about interacting with other characters and solving quests, which is important because that's what RPGs are traditionally all about.
Besides that, you also have the fact that weapons in New Vegas have stat and skill requirements to use properly, which adds far greater value and weight to your stats. In order to use weapons, you have to meet a specific strength requirement, meaning that if you want to use big weapons like rocket launchers and miniguns, you'll have to sacrifice stat points from other fields in order to pump up your strength. Even if you meet the high strength requirements, you'll also need to meet high skill requirements, thereby restricting powerful weapons for end-game characters. In Skyrim, you can get your hands on a Daedric Greatsword and start using it right away, which defeats the sense of difficulty balancing and leveling progression.
Then there's the fact that it's totally possible to max out all of your skills in Skyrim and unlock pretty much every perk you could ever want, all in a single playthrough. It's outright impossible to max all of your skills and stats in New Vegas (at least not without the DLC), and you can only pick 15 out of over 80 perks; this forces you to specialize your character in certain fields (role-playing a certain type of character, with benefits and disadvantages) and makes resource allocation a valuable, strategic element of the game.
Better characters and dialogue
In making Skyrim, Bethesda took a few lessons from their efforts with Fallout 3 and carried over a number of elements from that game. One aspect that made the transition was the inclusion of followers -- NPCs whom you could hire or persuade to follow you in your adventures much like conventional party-members. This was something of a welcome addition in an Elder Scrolls game, but the follower system in Skyrim is pretty bland and uninteresting. There are perhaps hundreds of followers to choose from, but none of them have any developed quests, personality, or functional impact on the gameplay -- they're essentially just pack mules to carry your stuff and lend a hand in combat.
In New Vegas, there are only eight followers to choose from, but those followers are so much more interesting companions than any NPC in the entirety of Skyrim. It basically didn't matter who you had in your service in Skyrim, apart from aesthetics; in New Vegas, each follower gives you a unique perk when they're with you, offering functional benefits to taking different companions. Each companion has a developed personality and has their own questline which progresses as you build your relationship with them, requiring that you say or do the right things in their presence and have them along for significant encounters in the world. They feel like actual people and serve significant roles in the gameplay and story.
When it comes to dialogue, there's really no competition. Obsidian is known specifically for their skills with dialogue trees, creating interesting conversations that actually branch out depending on your input and giving the player lots of ways to role-play within that system. Character interaction has long been an integral component of RPGs, and Skyrim just falls flat in this area -- most (if not all) conversations are entirely straightforward with only one, single dialogue option, and when they're feeling really sophisticated, they give you two options, which only branch the dialogue for the immediate line following your input, and then it converges back to the same branch.
Most characters in Skyrim feel completely lifeless and generic, and could easily be replaced by a quest board or a trade window without much of a loss. New Vegas characters, by contrast, have richer personalities and they make you care about even the most mindless fetch quests they sometimes send you on. I felt a deeper, more intimate relationship with Cass in New Vegas, a character you never actually romance, than I did with my own wife in Skyrim. I felt more endeared to a toaster in New Vegas than I did to any human character in Skyrim. I had more conversation options with a lightswitch in New Vegas than I did with even Ulfric Stormcloak in Skyrim.
Better replay value
Replay value is not an integral component to an RPG, but it's a sure sign that it was designed well. Replay value emphasizes character builds and role-playing, allowing you to play the same game in different ways depending on how you develop your character, how you solve quests, and with what factions you align yourself. When you can play a game two or three times all the way through and have vastly different experiences each time, you know for the sure that the game emphasizes your specific actions and decisions, shaping itself around what you do, which are important aspects for an RPG.
Simply put, I don't see Skyrim having much replay value at all because of how little concern the game actually has for how you build your character, and it only provides a scant amount of opportunities to solve quest in different ways, with very few conflicting quests allowing you to pick something entirely new. You can complete every single guild's questline in one playthrough, and upon replaying the game, the guild quests are going to be the same, straightforward, linear affairs as they were the first time around. Most quests don't give you any role-playing options, and it doesn't matter how you choose to the explore the world because nothing it designed to overlap in any significant or meaningful way.
The main bit of replay value I can see is siding with the Imperials or the Stormcloaks, but even that is pretty inconsequential in the grand scheme of things, considering how little impact those quests actually had on the game for me. There are a few other quests where you can do things a little differently, but for the most part they either don't alter the actual course of the quest, or the two outcomes are practically the same, anyway -- not enough of a significant difference to warrant a replay. Seems like the main (perhaps the only) thing a replay would affect in Skyrim is combat, which is itself pretty bland in the first place.
New Vegas, on the other hand, has four different main quest lines with four different endings and numerous different faction conflicts, allowing you to replay the game and experience tons of entirely new content, while shedding new light on content you'd previously experienced. Unlike in Skyrim, you can build your character to use different stats, skills, perks, and weapons (and find that the game actually plays differently), and you'll find more quests can be solved in different ways. Since the game has an intended path to follow with fixed stats and levels for every weapon and enemy encounter, you can use your prior knowledge of the game for some excellent, compelling meta-gaming.
It's also interesting to note that I got more playtime out of replaying New Vegas than I did in a thorough, exhaustive playthrough of Skyrim. Steam clocked my Skyrim time at 130 hours after I'd finished the main questline, did all of the guild quests, did all of the major town quests, as many sidequests as I could find, and as much exploration as I could stomach. Steam has my New Vegas time at 143 hours and counting -- I haven't even finished playing the game yet, and this is on a Legion playthrough, which has significantly less content to experience than an NCR playthrough. Granted, New Vegas has four DLC packs in its favor, so Skyrim will (most likely) eventually succeed that number of hours, but I find it an impressive notion that New Vegas manages to make less total content last longer, because of how complex and sophisticated that content is.