In a nutshell, Fallout 3 gives you a more polished package ready to go out the door. You can pop the game in VANILLA and enjoy it. Oblivion (Like Morrowind) needs a lot of help. Thankfully, help in the form of mods have been created in the truckloads, and can vastly increase your experience of Oblivion.
Fallout 3 is starting to pick up in the modding community however, so Oblivion definitely will be showing its age.
IN the end, I liked both games. If you're new to the either game, I would start with Oblivion. Playing Fallout 3 and then Oblivion will feel like a step backward overall, even a heavily modded Oblivion. Most mod work for Oblivion has hit a wall so to speak anyway, as now-a-days its pretty much making your characters look as "pretty" as you want them to. Namely, as slutty as you want them to.
If you just want a straight, no nonsense answer, then just go Fallout 3. There are already a few mods out there already that can vastly improve your first re-play, which in my opinion, is the funnest time in any rpg you play, because you now know the ropes and want to make the most optimized run though the game.