I originally bought the NVidia Shield because I needed a device that could do HBO Max and Twitch - and one of my consoles. Like, I don't mind streaming stuff on the console, but the interface for doing so on both the Xbox and the PS4 is garbage so I avoid it when I can.
I also really liked the idea of using it for retro-games, since it's got access to some decent emulators via the Google Play store.
The problem was it felt a bit jank. The "channels" on the main screen didn't work as expected, and would randomly go away. Apps would crash - not regularly, but often enough to be annoying. I got to the point where I was rebooting the Shield weekly, which isn't a huge deal but it wasn't ideal.
Chromecasting to it was laggy as all hell regardless of what was doing the Casting - bad enough that I ended up never bothering to use it. Apps would occasionally launch in a non-logged in state, prompting for credentials. Force quitting them and relaunching would fix it. This wasn't an every time thing, but often enough that it was a bit of a pain.
The final straw was when I had to relaunch the YouTube app three times, followed by a device reboot, just to get the audio and video to sync.
Honestly, it's a fine device, but all the annoyances added up.
The Apple TV is, in my opinion, a more polished product. The setup process for the device was simple (bring the phone close, then it's done), the setup for apps was mostly quick (either approve from the app on the phone, or login using stored Apple Keychain credentials), and the integration between iOS and TV OS is nice (phone works as a remote when you can't find the remote). It also paired with the TV much quicker, and training it to handle the volume was slightly less of a pain.
I've only had to reboot once, and that was for an OS update. I've not had to force quit anything - yet - and the apps seem to be either more stable or more polished.
Screen Mirroring, either from iOS or MacOS, is much quicker and more usable.
I'm not a fan of the tiny remote - it's much too small, and I don't dig the touch pad. At some-point I'll replace it with a third party remote, but I haven't done so yet.
The Shield does some things better than the Apple TV - I do much prefer the Shields home screen (when it worked correctly) to the Apple one, it can "do more" with regards to what sort of games and stuff it has access to, but overall I've had less frustration with the Apple device.