To get an iPad and an iPhone talking to each other you will need to implement the optional delegate method:

- (GKSession *)peerPickerController:(GKPeerPickerController *)picker sessionForConnectionType:(GKPeerPickerConnectionType)type {
return [[[GKSession alloc] initWithSessionID:@"ApplicationSessionID" displayName:[NSString stringWithFormat:@"iPad - %@", [[UIDevice currentDevice] name]] sessionMode:GKSessionModePeer] autorelease];
}


Otherwise they will not find each other as they are different application. Hope this helps, had me scratching my head for a while.