I had an interesting introduction to the games, so it is sometimes hard to differentiate the two. I found myself wondering if Sulik was in Fallout 1 or 2 the other day. I was sure that he was in 2, but I was unsure enough for it to be funny. My uncle had both Fallout 1 and 2 but I hadn't heard of them at the time. Fallout 2 had just came out so my uncle had save files for both games which were on my Grandma's computer. He was pretty excited about it - he introduced me to a lot of good games, so I knew I was in for something special. Hell, he introduced me to Lunar, Final Fantasy 6, and Fallout 1 and 2, among many others.
So he asked me if I wanted him to spoil the ending to Fallout. Merely to show how interesting the game could be. I said alright. He loaded up the end of Fallout 1. The conversation with the Master. He exhausted all the dialog options making the Master kill himself in the process. I was amazed. I had never seen such a game before. Up to that point I had only played a few jRPG's since I was young and didn't have a PC at the time.
Fallout 1 was the first thing I played. I remember getting to Junktown with my uncle guiding me along off and on, as he chatted with the rest of my family. I chose to take out Gizmo in my playthrough. That moment is definitely a high point in the series. Necropolis is an insane location. I loved zombies at the time too, so it was the coolest thing I could imagine - zombies in a role playing game! Of course my uncle quickly reminded me that some of them are good. These weren't zombies. They were alive. The gore really helped to pull me in. There is nothing like a burst shot exploding Ghouls to bits. The only thing that killed it for me was the bugs. It botched several of my initial gaming sessions. I didn't truly progress until he gave me a disc that I took back home to our new PC.
Fallout 1 does have a tighter story, but that does leave it on the short side, leaving you to want more. Fallout 2 scratches that itch pretty easily, but some don't like the wacky stuff it introduced into the series. I never had problems with that. I love New Reno. The ghost never bugged me either. Nothing can top either one of the first two Fallout games anyway as far as I'm concerned, but if I had to choose between the two, I would choose Fallout 2. It has more to offer. The game plays better. Companions aren't a bitch to deal with. Then you have those three magic words that make shit go to the next level; Killap's Restoration Patch!
On the other hand, I hate some things about Fallout 2, which is purely due to them rushing it out. San Francisco is completely empty. There are a handful of items in the entire city. It is fairly secluded, so trade could conceivably be an issue, but it's obvious they had a separate team on it when compared to New Reno or The Den. There are a few places like that.
It really comes down to - do you like Mutants or the Enclave better?