They are both CRPGs so inevitably there is going to be some crossover between fanbases.
Not convinced there is much influence directly attributable to FO3 in Skyrim.
Level-scaling appeared in Oblivion, it was improved in FO3 but is hardly a Fallout feature.
Perks in Skyrim don't look much like perks in Fallout 3. Sure you get 1 per level but they are all skill related and seem to be organised into perk trees. The main thing they have in common is the name.
Hopefully Bethesda learn something from every game they make so I'm not surprised there is some FO3 influence, I just don't see much.
Just like they improved level scaling in Oblivion, so do I think they will improve perks in Skyrim. While the perks may not look like the perks from FO3, which is a good thing given one has guns and the other swords and magic, the influence is undeniably there.
BTW, Kiralyn, you give me no credit by saying I wouldn't have made the connection if perks had been called something else. Although, since they are called perks, your point is moot. And, yes, I completely agree with you in that the companies do learn from making other games. I hope they took notice of some things from Fallout and used them to improve Skyrim.