As far as I understand, GameKit provides Bluetooth-maches, while GameCenter allows to play matches through internet. So it looks like the best scenario is to use both of them? Is this reasonable?
I know this answer is a little late, but...
Game Kit is the name of the framework that you use to add support for Game Center in your game. Game Kit is the developers interface to Game Center.
You can read more about this here: http://developer.apple.com/library/ios/#documentation/NetworkingInternet/Conceptual/GameKit_Guide/Introduction/Introduction.html