I did some experiments using Plex Media Server on an i3 (dual core) - all over wire via a Mikrotik CRS125 switch to an ATV4 and also to a Samsung KU6000 running Plex client. Content was 1080p H.264. Stuttering occurred at 80 Mbps point playing back at native resolution to both devices. Using Plex to transcode high bitrate content to 20 Mbps was best.

 

Also tried Fuse on the Apple TV to play back via SMB share. Again stuttering occurred at 80 Mbps.

 

I know that ATV4 only has Fast Ethernet interface but do the TVs have GbE wired interfaces??