Game Center is Apple's iOS only feature.
Google has Play Games, which is an Android only feature.
So no sharing of saved game data between the two platforms.
I've been a bit addicted to SimCity Buildit recently, which uses both to sync data. But my Android devices only have access to the saves in Play Games and my iOS devices only have access to saves in Game Center. So I have two different cities going because of it.
It would be cool if Apple and Google would link the services together, but obviously that will never happen. In the meantime some games will just have to use their own cloud service if they want to be completely platform independent, like The Simpsons Tapped Out does (uses EA Origin).