I can't speak for atv 4 but HBO go picture quality is consistently garbage on my atv 3. It certainly is not nearly 1080p and is probably somewhere just above 480p for me.
I have it hard wired cat 6 directly to a fast fiber internet connection, that will send Netflix to 4K in seconds.
It is so bad that I cannot even watch big movies streaming because it looks like I am watching a Chinese bootleg.
They really need to step their game up if they want $14 per month. The torrents from broadcast look much better then the streams.
Every other service is the opposite. Watching shows on the fox app for instance are in beautiful 1080p quality that beat any cable box.