Yup, both Shield and my TV support HDR
The only way I can see Apple TV offering better picture quality, is if the shows are provided by Apple TV themselves at some sort of higher bitrate streaming quality...like if you stream a show or buy a movie from iTunes...or whatever they are using these days...and their versions are encoded at a higher bitrate, then it will look better.
But, given the same source (ie. Netflix, or whomever), quality should be exactly the same (ie. whatever the top quality the streaming service offers).
The above reply is barely English, and I apologize in advance.
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