Mike Tyson will FOREVER be remembered for that ear bullshit. Hey, you bit off someone's ear, you're GOING to be remembered for it--always good for a laugh, I say! Dated or no, I love the humor behind both FO games--there's so many things to this day that I'm finding hidden in there that I didn't know before.
I agree that the biggest difference between the games is the focus of the story. FO1 focuses on the lone wanderer, and Vault 13; whereas Fallout 2 is more focused on the world at large. Sure, you need to save your village but in the end, it comes down to a world-saving plot, and the focus is obviously the chaos in the world at large.
THEN you have the gameplay mechanics--a longer timeframe to play the game (I always thought FO1 was a bit on the short side). As others have said more companions, I believe there's more secret encounters too; I'm pretty sure your base stats and perks are the same, but I'd have to look for myself (it's been a while since I've played FO1. Years, tbh).
All in all, both games are great, and both are very similar. I'd have to agree that focus is the biggest difference, much like the narration of a book.