2/NV for Fallout and Morrowind/Skyrim for Elder Scrolls.
Fallout 1 was... well, it was a learning experience. It was good overall but it had some mechanical weaknesses and a dearth of meaningful content compared to Fallout 2, which fixed many of the broken mechanics and had generally more interesting content, not to mention much more of it. It also had that jokey tone which a lot of people hate but I thought was great, compared with Fallout's efforts to be super serious in a campy world of comic-book science and 50s fauxstalgia. Ironically, Fallout 2's story and settings actually seem more suited to a serious story. More epic, more dramatic.
I haven't played Fallout 3 but cursory inspection makes me feel similar to my thoughts on Fallout 1. Mostly good, gameplay is still something of a work in progress, tries to be way too serious in tone. Setting it on the east coast also hurts it: Fallout as a series relies on a consistent, connected canon for its identity; otherwise it's a pretty generic wasteland. Fallout 3's setting is too distinct, culturally and geographically, for there to be any substantial connections to the other games, while those that are there (Enclave, BoS, Harold, Super Mutants) stretch suspension of disbelief with their presence.
New Vegas, then, is Fallout 3's Fallout 2: better design and mechanics, slightly goofier, and more substantial. The fact that it's back in the west is also a plus. I concur, too, that its DLC is excellent and proof that it's not inherently evil. I don't like the way each NV DLC feels a bit like a separate game with the same engine, but they're fairly enjoyable in their own right. I have one small criticism of the game's main plot, which is that Caesar's Legion is strawman evil and mechanically disadvantaged to the point where siding with them is for masochists or people deliberately roleplaying jackasses.
The first two Elder Scrolls games aren't really Elder Scrolls games as most people conceive of them. Their settings are barely connected ("Nuh-uh! They have the same maps and mostly the same races and that's all that matters") and they're mostly randomly generated and kind of boring. Let's get those out of the way.
Morrowind is the most interesting Elder Scrolls by far in terms of setting and lore. Every other Elder Scrolls game is at least a little generic, but Morrowind is pretty much antipodean to Tolkienesque fantasy with its giant bugs and reptiles, bizarre mythology, and interesting political situation. In terms of gameplay, the high complexity and possibilities for emergent gameplay are wonderful but the combat is pathetic and even more than Fallout 1 and 3 feels like a huge work in progress compared with the more polished 3D Elder Scrolls games. It's basically Baby's First RPG Combat System with its God-awful anachronistic dice mechanics and overreliance on stats. I realize all RPGs have some degree of stats, but with Morrowind player skill is borderline irrelevant.
Like Fallout 3, I have not played Oblivion. Like Fallout 3, it looks okay. Fortunately my big complaint about it is one that doesn't require actually playing it: it's too fucking generic. It's so fucking generic medieval western RPG tropefest that they actually retconned the older games' lore to make it more fucking generic to pander to people who want really fucking generic games. Second, based on videos of it, its graphics are meh. I think it was too ambitious. Morrowind had shitty graphics but it pulled them off because they realized the limits of the time and stuck with them. Skyrim actually has the technical ability to pull off facial animations et cetera. With Oblivion they tried to do more than they had the technology for and wound up with the uncanny monstrosity that is Oblivion's facial animations. It also had horse armor DLC which is a possible patient zero for the modern pandemic.
Skyrim's setting and lore are much more interesting than Oblivion's even if they don't match Morrowind in their originality. Obviously, its graphics are borderline godlike and its modding potential through the roof compared with the older games simply because it's newer and more advanced. I also think - fight me, hardcore RPG people - that it is the mechanical apex of the series. I have never been a big fan of traditional RPGs because to me (emphasis: to me) character stats are kind of boring and their excessive application in video games is a relic of the pen and paper era.
Skyrim's streamlined stats that get hardcore RPG nerds riled up about the series' "casualization" are an enjoyable middle ground: they play enough of a role that you get a firm sense of progression, but not so much that you have to agonize over where to distribute points; they give you choice as to what skills you want to emphasize, but don't make you overspecialize by arbitrarily splitting up weapon types or schools of magic; they factor into gameplay, but not so much that you have to worry whether you even hit the enemy because your skill is too low.
In the end, I think Fallout 2 and Morrowind are the most interesting in their series, while the newest games - New Vegas and Skyrim - are the most fun to play. I can't really say which of these aspects I value more, so I won't give a definitive favorite.