When levels and characters get loaded on your system, you’d be hard pressed to find a difference between Disney Infinity 3.0 on Apple TV and Disney Infinity 3.0 on any other platform, aside from the obvious benefit of graphical fidelity on more powerful systems like the PS4 or a Windows PC. It took me staring at video side by side to tell any substantial differences.
When levels and characters aren't on your Apple TV, the results can vary dramatically. The Apple TV version’s loading is significantly pronounced compared to systems like the PS4 and Xbox 360. There’s no disc in a tray to stream levels from. There’s only the internet and internal storage that Apple TV manages and the internet’s nebulous cloud, from which the game loads levels.
To be fair, though, I've spent a lot of time with Disney Infinity 3.0 on four pieces of hardware during the last few weeks. Loading screens are par for the course — though, again, they're pronounced on the new Apple TV, almost certainly because of tvOS' app restrictions.
But, again, once you’re in the game, you’re really in the game. As in the real Disney Infinity 3.0, full of dialogue, voice acting, gameplay — all of the things that you’d expect if you were playing it elsewhere.