Long post incoming.
I love the Fallout series. I, along with many other people started with 3, and at first I found the game to be boring. From what I understood, it was just a game where you talk to people and the killing didn't occur until you talked to over 200 people or so. While this is true, my 13 year old mind didn't like this, and I went back to CoD about an hour into to game.
I eventually came back to it in the summer of 09' and I have to say, it became my favourite WRPG of all time. I played it throughout summer, finding every nook and cranny, becoming ridiculously strong, and having so much fun with the game Achievements didn't matter. Fallout was amazing to me, the atmosphere was one of the best parts of the game, it immersed me so well with the amount of lore, and the music. Walking past some destroyed buildings, with a huge sign advertising the vaults, with some dead skeletons on the floor, and around the buildings, while this
music played. It was an incredible experience, and it was one of the many things that blew my mind in vidya. I loved walking around the wastes doing nothing but looking at the destroyed buildings, reading/listening to old documents from the old world, and in general having a great time, imaging the time before the war, and before the aftermath.
Fallout 3 was an amazing game, and I still have it in my top 10 RPG's of all time...
Then came Fallout New Vegas. At first, I disliked this game a lot. I thought it was a smaller, weaker expansion to the Fallout series, and I would never play more than the Main story before I quit, but then I got it for Xbox, and played so much out of it, I have over 500 hours clocked on that game. It didn't have the atmosphere Fallout 3 had, but it was overall a better game in my opinion. The amount of things Obsidian added to the game made it a much better game than I thought. New Vegas is like Fallout 1, 2 and the engine and gameplay of 3 put together. It was such a brilliant game, and the amount of things you could do added to this fact. The locations, the quests, the fallout humour. It was all there, and made the game brilliant because of it. In my opinion Fallout New Vegas is the best Fallout game, mostly because it feels like a true sequel to 1 and 2, and in general is an amazingly good game.
I replayed the original Fallout in 2011, with the intention of actually completing it. At first I disliked how it played, as many people did. I found the 2.5D turn based combat to be repetitive, boring and incredibly unfair, but after all this was put aside. The game become much more fun, and just like 3, and NV. I enjoyed it. While it didn't have huge impact on me, since it was quite old. It was a brilliant game to play and was very fun, and I would love to see a Fallout game using this style again, even if it is outdated.
Fallout 2 had the same appeal to me, except there was so much more to do, finding Vault 13 again, and becoming ridiculously powerful again was also a lot of fun. Fallout 2 was so much better than the original improving in many different ways. Fallout 2 is brilliant, and feels just like a 2.5D version of New Vegas.
Overall, I'd rank them
NV > 3 = 2 > 1