I've looked at this a few times, and AppleTV actually has pretty poor support unless you're only using a select few streaming services and not streaming any of your own content. Shield performs exponentially better in every way except for the god awful stock interface (and Google data collection vs Apple data collection). The hardware and tvOS still have extremely limited support for most video codecs, no support at all for audio pass thru, and very limited non-stereo audio options. If you want the equivalent of watching on your laptop it's good, but if you have better than stereo speakers, or a 4K TV that supports HDR10+ or Dolby Vision, AppleTV can't compete except for the big name streaming services that have special tvOS privileges/integration.

FWIW, I have no trouble playing any of my alternatively sourced media, 4K Dolby Vision included, using an app called Infuse. Pass-through audio may indeed be an issue for some lossless surround formats, or at least that's what it sounded like the last I looked into it some years ago. I don't have the right room to set up surrounds so it's stereo only over here anyway. But that said I love the app, lovely interface, etc.

> a 4K TV that supports HDR10+ or Dolby Vision, AppleTV

You can play HDR10+ 4K on Apple TV using Infuse[0] (and whatever DLNA server you want to stand up with your content.)

[0] Since 2017, apparently.

I stream all of my own content with an Apple TV and Plex just fine. I don't know what problems you've had there. It even handles exotic stuff like Hi10P h.264.