I'm an Oblivion fan myself. Don't get me wrong, I enjoyed Fallout, and the combat in Fallout was better. However, Oblivion had (by far) the best loot, and for me that was a big selling point. I just liked traveling the world getting as much awesome shit as I could (often by stealing it) and putting it on display in my houses (that's right, in Oblivion you get more than one!). Don't ask me why, it was just fun. Also, unlike in Fallout (where most unique weapons just had better stats), in Oblivion unique weapons actually looked unique. A minor complaint for some, but for someone like me who really enjoyed the collecting aspect of the game, the fact that unique weapons just had a different name and better stats (in Fallout) was really disappointing.
I would say that I also liked the Oblivion world better. It didn't feel like a wasteland (yes, I know the other was supposed to be a wasteland, but I prefer the aesthetic and feel of the Oblivion world).
So I suggest Oblivion.