I like that in Fallout 1, there are seemingly 3 stages instead of just 2. And the best part is you can complete each stage in any order you want to. The Fallout 1 formula was "You have a small goal, okay now you have a big goal, now an equally big goal. Replay and do these in any order if you want." now it's "You have a small goal, now you have a big goal. This is the order you must do it in, in every playthrough.". I like how compact Fallout 1 feels, there's only a few locations, almost every location is tied together somehow, and it seems like everything you do has a weird feeling where you did something big but not really.
However, I like Fallout 2's story and writing. Not that I dislike Fallout 1's, Fallout 1's antagonist was the best in the series. It's just I like the idea that you're apart of something way bigger than yourself, plus each of the new factions in Fallout 2 are really cool. And though not each location is tied together, each location feels unique and meaningful, even Modoc which is a completely optional location in every type of playthrough. I also think the companions in Fallout 2 are way better than in 1, each has a more thorough backstory and personality.
In the end, I like Fallout 2 more than Fallout 1, but not by a lot. The main reason being: In Fallout 2, you can become a porn lord.