On a black iPhone 4, I open the Game Center application and it is stuck on "loading":

For a moment I assumed that it was a problem with Apple. Well, no, because turns out I have a white iPhone 4 where Game Center does work.
I heard that if an iPhone is jailbroken, you can't use Game Center for developing applications on sandbox mode. However, it does work for normal games. Both of my devices are jailbroken.
Why might my black iPhone be stuck on "loading" within the Game Center application, while the other device works just fine with it?
There is a difference in iOS version though. The black iPhone, which is stuck on the loading screen, is 6.0.1, while the white one, which works, is 4.3.3.
I already tried rebooting the black iPhone and killing the Game Center application.
