If you're coming to the original Interplay
Fallouts for the very first time, I'd suggest starting with the first game, playing it through, and then starting
Fallout 2 only afterwards. Not that
Fallout 1 is a bad game at all, but rather because so many improvements were implemented in the sequel that you might have a harder time enjoying the first one if you play the second one as your initial experience.
Which is
NOT to undersell the incredible achievement that
Fallout 1 is one scintilla, however. Far, far from it, in fact. You're gonna have a blast with both.
I'd have to say that I prefer Fallout 1. I always found the story of Fallout 2 (more specifically the Enclave and Vault experiments) to be a bit contrived, and the setting was treated in such a lulzy way that it felt more like a parody of Fallout than an actual sequel. Granted most of the RPGs of the 80s and 90s were a tad bit more tongue in cheek than the serious business RPGs of today, but Fallout 2 took its humor a wee bit too far.
Fallout 2 has more stuff to do, but it's debatable as to whether or not that stuff is any good. Fallout 1 had a better storyline, a more balanced portrayal of the setting, and generally more enjoyable side quests. I will give credit where credit is due though; Fallout 2 was way more difficult at the beginning than the original Fallout.
Many old-school folks give Bethesda crap for supposedly "gutting" the humor elements from
Fallout 3, but in my book, they simply scaled it back to the far more appropriate (and palatable) levels of
Fallout 1 -- the second game got a tad goony and overbearing with its pop-culture humor at times, and in my eyes this was merely a return to the series' initial roots.
Also, it should be noted that after the bulk of the original
Fallout 1 design team quit Black Isle early in the development of Part 2, the game was split into two separate development "chunks," with a different design team handling each half (and frequently not knowing what the other side was up to). When the final development phases were underway, the two halves of the game were stitched together for the very first time, and -- quite amazingly -- they meshed/integrated extremely well together. You wouldn't even suspect that
Fallout 2 was actually two separate designs, playing it...the blending really is that good, although some inconsistencies come through occasionally.