I've used both, still prefer the shield. Hardware-wise they're about the same insofar as I never had trouble with any lag at any point on either. This is what sets both of them apart from all other streaming devices. Chromecast, roku, fire sticks, they've all had trouble with some of the higher bit rate media on my jellyfin server. Apple TV and shield did not.

I prefer the shield remote.

The main difference comes down to software. Android TV is simply better. I can get the interface exactly how I like it, and run all manner of apps in the background, making the remote more useful among other things. Apple TV doesn't even have access to the jellyfin app, you have to use swiftfin on the app store which has issues. You can sideload apps super easily on the shield. (Though for the jellyfin example, you don't have to. It's on the play store.)

Developer mode is also a great thing to have on the shield. I can now transfer apps and media from my pc super easily, speed up animations to make it feel snappier, (a feature sorely missed on apple TV) or even remote control the shield (which I haven't found a need to do yet so I'm not counting that as a plus).