They are both great games. And both different types of RPGs. High fantasy vs. Post apocalyptic. I love Fallout 3, New Vegas and TES V: Skyrim. I just spend much more time in Skyrim. Much more actually.
Here is one thing that Skyrim doesn't have that Fallout does, which hurts Fallout for me:
Level Cap.
Once I hit the level cap in Fallout I lost a lot of interest. Almost killed the game for me. I still finished the main story, but no longer cared as much for the side quaets and stuff. I know they put the cap in there for balance sake, but it still hurts me whenever I see I should be getting XP, but I'm not leveling up.
In skyrim there is no level cap, you can make skills legendary and basically keep leveling up forever.
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elder scrolls lore >>>>> fallout lore
For sure!
Also, the Dragons in skyrim speak their own fucking language. In Fallout the fucking rad roaches don't talk. pffft...