I have both Apple TV 4K and Nvidia Shield TV. I am a new user of both, so still learning. The setup that I have is a 4K HDR10 Projector (no Dolby Vision), Denon AVR with 5.1.2 Dolby Atmos/DTS:X. The content I watch - 60% of the time, my ripped Blu ray content; 40% Netflix, Amazon Prime, YouTube. (I am in Dubai, so most of this Hulu, HBO Now kinda content is not available here, so doesn't matter to me). Features important to me: lossless object-based audio, 4K HDR video. Would like to use one device for everything, if possible.
I ended up using both devices for my requirements. Apple TV - because only this device gives Atmos over Netflix app (Shield doesn't, even after the latest OS update that happened yesterday). For everything else, I use Shield - it gives me Atmos over Amazon Prime (Apple TV as well), plays 4K in YouTube (Apple TV doesn't), plays 4K HDR videos in my network attached local hard drive with audio passthrough to my AVR enabling Atmos over True HD and DTS:X (through Kodi App) (Apple TV doesn't). I had a Sony UBP X700 Blu ray player, which I ditched because it doesn't play Atmos over MKV files (although it does play Atmos over M2TS files). Shield does both.
So in a future update, if Shield gives Atmos through Netflix - then I don't need my Apple TV anymore.
In a future update, if Apple TV supports lossless audio passthrough for apps like Plex, Infuse, and it starts supporting 4K in Youtube, I can ditch my Shield.
But, let's say if both happen, I will probably keep my Shield than Apple TV. I like the user interface of Apple, but would prefer the flexibility of Shield. Two other minor points in favor of Shield - it comes with a USB port and built-in chrome cast. Both, I don't have much use now, but good features, especially since I have an android phone. One point in favor of Apple TV though - the iTunes movies database is much better than Google Play Movies. You will find many 4K HDR Atmos titles in iTunes for rent and own, than in Google Play.
The parts I missed because I don't use them at all - Music, Games. Not the best person to comment, but looks like Shield have an advantage when it comes to Games, and Apple TV on Music.
So bottom line, as many already pointed out - you just need to list down your needs by priority and choose the one ticks all the boxes, if its really about one vs other. Else, if you don't mind spending some extra bucks, buy both.