Wow, it seems a couple of people don't really understand the Fallout setting. In the Fallout setting, everything is what people in the 50s dreamed about: Nuclear powered cars (I believe Ford actually made a mock-up back then), servant robots, infinite optimism and believing that science will fix everything by default. It also follows the logic of 50s horror movies, where stuff got bigger and meaner when it was irradiated. Thus, you have giant scorpions, giant mutated people (super mutants) and giant everything, really.
As for the two games, I have to say I have spent countless hours in both. But Fallout ultimately wins because oblivion wasn't very free when it came down to it: Caves involved in quests would be locked at some points if you didn't have the quest, you were rarely rewarded for exploring like you were in Morrowind, and the difficulty adjustment also hindered you in a way (why be level 200 when I can do everything at level 1?).
Other things to nitpick about Oblivion is that while it DID have a lot of quests, most of them were over in a few minutes because they were basically fetch quests. Some also didn't make sense at all. How much magic did you ever use in the mages guild? One is getting a book from a mountain top, one is helping with a prank (regular stealing), one involves being undercover (magic use is optional), one is fetching a staff, one is fetching a ring, one is fetching an amulet and then I can't remember the others if there were more. You did get to use magic a little at the university but once you're in there, you've already won the game due to custom spells. Frankly, the balance in the game sucked, but it ultimately was the freedom thing that discouraged me.
Fallout almost always motivates you to do stuff on your quests. Locked rooms, locked containers, stuff tucked away in corners and such always kept you wanting to check it out. You can find notes hinting of loot, make custom weapons from stuff you find and sell scrap, all of which keeps you on your toes for stuff. Outside quests and a few specific encounters in Oblivion, you were stuck with rusty swords and such until you levelled up sufficiently. It wasn't you having to level up to face a challenge and get rewarded with better gear, it was you working to make the monsters better. It might be a challenge for some who want to see all the gear and possible monsters but for me, it was simply like having another job.