I don't understand why she freely gives it to whomever does have a favor in Oblivion, but in Skyrim, Karliah tells you no one should have it.

Something to do with the conduit to Nocturnal's realm being shut down without the Skeleton Key, causing every thief to 'run out of luck'.

Skyrim's TG = Another case of bad writing. Why can't we kill Karliah and keep the Key.

Oblivion Nocturnal: Thanks ma'man, take this awesome lockpick as a token of my appreciation.

Skyrim Nocturnal: Return the slaaaaab, or suffer my curse...