First: Setting-wise Fallout 3 and Oblivion have absolutely nothing in common. The entire concept of comparing them fails there.
Second: The only thing in common between them is the engine. Gameplay-wise Fallout 3 is a far cry of Oblivion, even if they share some buttons here and there.
Third, Fallout doesn't have drivable cars nor mounts.
Fourth, If you know nothing about Fallout pay attention to the intro and what people tell you. As a first "warning" I note that this game is retrofuturism: Fallout is what people in 50's mostly believed future would be. There is Jazz, nukes, tip top dresses and laser guns. Power Armor, vengeful US government holed up in a bunker, a techno-religious boyscout group known as the Brotherhood of Steel and so so much more.
Fifth, yes Fallout 3 has "caves". Not many "caves" as in underground rocky dungeons, but plenty of buildings, bunkers and city streets to stroll on a saturday morning. Complete with super mutants, of course.
Personally I detest Oblivion, but then again it's the only TES I've ever played. Very poor dialogue, lousy story, candy colored world, and annoying balance system... Fallout 3 has none of these traits, even if the dialogue is indeed lacking in some points. But overall the story is coherent and you won't notice many real flaws unless you have some specific preferences.
If you like Fallout 3 I recommend Fallout 1, 2 and New Vegas. All excellent games.
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NOW and
TODAY for the
ENCLAVE. Restoring America's Future Today!
YOUR future.
Unless you're a mutant...