Of the two, which has the earlier release date?
That depends on if potential AppleTV updates can transform the current AppleTV into an IOS game system - they may well be able to, the main thing would be Bluetooth LE support for advanced controllers. Don't forget that out of the gate an Apple TV with game support would have games and scads of controllers thanks to the iPhone.
Even if the current AppleTV could not support it, we could easily see an AppleTV capable of that well before the XBoxOne launch - even if Apple didn't explicitly make it a game system.
Lastly, the AppleTV is already kind of a game system for many since you can use AirPlay to send a game display over AppleTV to your TV. Combine that with the new controllers and you wonder if Apple really needs to make the AppleTV a game system, or if they can just keep it as a gateway between portable gaming hardware they already make, and your main display...