I'm a fan of Fallout 3 (not necessarily as a sequel to FO2, but as a standalone Fallout game). I was a little hesitant about New Vegas because it looked just like a re-skin of Fallout 3. However, after spending about 15-16 hours with New Vegas so far, I will admit I'm pleasantly surprised. In case anyone is on the fence, I'll attempt to round out the similarities and differences between the two games.
Let's get the obvious stuff out of the way - Yes, it is basically a re-skin of Fallout 3. The graphical engine is basically unchanged. There are new weapons and new clothing/armors and the world looks a bit different due to the different setting for the game, but by and large it's Fallout 3 in the visual department. This of course means that PC users with good rigs will have to wait for mods to pretty the game up a bit. There are already good lighting and shader mods (I tried them last night and the difference is quite considerable, the mods add a lot of atmosphere). The high-res texture pack is not out yet, but you can count on it coming. There are a couple misc high-res weapon reskins, I saw a blood texture, and a couple armors.. the world textures will come pretty soon, I imagine.
Now, for the not-so-obvious. Bethesda, in my opinion, has been good at crafting massive worlds, but not so good at making them feel real. In both Oblivion and Fallout 3, there were countless caves and such that served little purpose other than getting xp and loot. The world in Fallout 3 didn't really feel alive.. all the outposts were completely disconnected and had nothing to do with each other and I just never felt like there was anything actually *happening* that wasn't caused by me. Obsidian, on the other hand, seems to have paid attention to the atmosphere of the game. Of course there are still caves to find - I found 3 in about 30 explored locations, so the frequency is much reduced and you're not thinking "Gee, *another* cave!". A lot more of exploration is now sight-seeing, which is nice because those tend to be more varied and provide a nice mix between sight-seeing and combat.
At the same time, the addition of factions to the game gives rise to stuff just happening and interconnecting events. The major factions have their stories so you can understand their motivations and actions, and aren't just "there". There are, of course, minor factions (like individual towns) that mostly just mind their own business, but even those towns feel like a natural part of the world because the presence of factions creates world-encompassing events through no action of you the player, that these towns are all a part of and all can reference. How you interact with these factions makes a difference in what quests and options are available to you later on. Very soon after starting the game, you are introduced to two factions, and if you are inquisitive enough to find the quest buried there, you will soon find yourself making a choice, which might just have a big influence on how you can finish another, totally unrelated quest (I know this is vague, but I'm trying to avoid spoilers).
All in all, the world in New Vegas just feels more cohesive, like a living and breathing world that you're a part of as much as you are shaping it through your actions.
Then we have the introduction of crafting in to the game. You can make food, drink, ammo, guns, you name it. The crafting options are based on your related skills (food/drink need Survival, chems and stimpacks need Medicine, ammo and such needs Repair), and you start with a very healthy list of recipes. It is perhaps not essential to gameplay, but especially if you are playing on Hardcore mode (more on this later), it definitely helps. The nice touch, I thought, was that as you use weapons you end up with empty ammo casings (or depleted energy cells/fuel canisters/etc) which you then use to make new ammo out of. You can of course find these on merchants and as loot. You can also break down weapons and ammo for parts you need for other stuff. All of these require their own "site" (Workbench, Reloading Station, Campfire), which can get annoying to track down as you move forward - especially campfires that seem to be pretty rare.
Then we have the Hardcore mode, which I think has been pretty overblown in the reviews. What it basically means is that you need to drink, eat, and rest occasionally, heals are over-time and not instant so that you can't pump yourself full of stims during a fight and be at full health in a second, and ammo has weight. These are quite a bit loosened.. I've gone days in-game without it telling me I need to sleep, I never get hungry because I use food to heal, and I just have to make sure I keep some dirty water (a little bit of Rad) or purified water on me while traveling for dehydration. If you're trying to fast travel and something terrible would happen (dying from dehydration, or something), it just won't let you so you can't have an accident happen. Ammo having weight does introduce tighter inventory management, and can be a little bit of a hassle.. but that's because I like carrying 10 different weapons each with their own ammo. In short, I think it's actually pretty fun to play in Hardcore mode, but it is separate from game difficulty and can be toggled on and off later (after the initial presentation in-game) at will.
There are also companions that can follow you and you have some control over (unlike FO3), however I haven't gotten one yet so can't comment.. however, it's something FO3 didn't really have at all save for a few story quests.
Oh, and Obsidian also left several nods to the old Fallout games, which earn New Vegas lots of Awesome Points from me. I've already met the (very aged) pilot who ended up crashing her Vertibird outside Klamath, as well as the niece of the woman from Modoc who chained up a female Deathclaw and served Deathclaw Omelettes. These kinds of things are just awesome to see.
In short - even if New Vegas has no graphical improvements over Fallout 3, and the same engine issues - it is hands down a more polished and whole game. It even feels more like a Fallout game than FO3 did, due to how the world atmosphere was set up and there's more interaction between its various denizens.