I loved the simplicity of Fallout 1, and how you could finish the game with an overall great character without having to gain as many levels. Of course, simple isn't always great, and that is why I also love the long gameplay that Fallout 2 has. Story-wise, Fallout 2 has a more intricate story that has complexity surrounding it, especially with the various endings for each town (which were a pain in the @SS if you ask me, but that also rendered it a sense of rpg-ism) and the new "setting" (albeit, at a further date than the first one, which was soon after, if not almost immediately, after the war in 2077). I'm pretty sure that the makers gathered for a few months to come up with the new story, which added different elements based on what they thought was happening elsewhere around the southwest region of the US at the time [of the game].
Gameplay-wise both were great. Fallout 1 had less stuff to play around with, but delivered a great gameplay nevertheless. Fallout 2, on the other hand, had tons of new stuff for one to mess around with, and create diverse characters (much like an mmorpg would offer now, except in Fallout 2 there's no online play!). I will continue my reply at a later time, since I have a lot to write about and it might seem too big for just one reply, hehehe.
I will say one more thing: all in all, both games were awesome, and should be on everyone's library of owned games.