Skyrim is the best game ever I'm serious y'all needa buy it it's got dragons and it's fantasy and it's got trolls and frost trolls and vampires and werewolves. It's amazing and I would recommend it to anyone.
Story wise, they couldn't be any more different. They are both first person experiences though which is probably the biggest similarly between the too. There isn't any character customization in the Bioshock games and the story lines and game play are a bit more linear than Skyrim, but they are still really incredible gaming experiences with compelling story lines and beautiful settings to explore, just like Skyrim is. I'd recommend giving them a try! :)