I've tried placing the files on both a Windows Server (SMB only) and my Linksys Router/Shared USB device (SMB and DLNA) with same results so I'll talk about this with the files sitting on a Linksys EA6900 router via a USB3 external hard drive. I'm connecting to my Apple TV using Wireless AC and have tested it to deliver 90 mb/s consistently. In comments below I have tried changing the network latency options in both directions with no noticeable differences.
The DJI Phantom 4 files I am trying to view are 1080 @ 30 fps, examining these files the bitrate is indicated as variable but I note that it's almost always a consistent 40 mb/s. When I try to view these files using SMB they do play but are very herky jerky, stuttering every few moments. When I view via the DLNA (a builtin Twonky server) on the same device/connection they play much better but do still occasionally stutter. Here is a link to a smaller sample file directly downloaded from my Phantom 4 at approx 500 MB.
http://picturesbyalex.com/DJI_0947.MP4
This same file when I attach using my ancient WD TV Live box plays perfectly. I can also view it from a old laptop using SMB and Windows Media Player and it plays just fine.
Now - just to add some more data to the mix; I took that same file and used TMPEGENC to add audio, a music track, and while reencoded TMPEGENC decided that it only needed 12.25 mb/s bitrate (I didn't even notice). The output, to me, appears to be identical. This file does play without issue via VLC and Apple TV. That file is: http://picturesbyalex.com/DJI_0947_modified.mp4
One of the biggest reasons I bought Apple TV was so that I could retire my WD Live Live box for streaming files from SMB and the majority of the files I have (hundreds) are these DJI drone files. The 4K video @ 60 fps have bitrates of 60 mb/s. The WD Live plays them just fine, VLC barely. I know that I'm not reporting a bug, per say; but I'm hoping by providing you some information you maybe able to look and see if there is a way to irk the same performance out of a ancient single processor WD Live box from a modern dual processor Apple TV box
Last bit of info, the ONLY other video streaming app on the Apple TV App store (and yes I bought them all, sigh) that comes even remotely close to VLC is FileExplorer for $5. It plays everything smoothly and has a great interface and accesses lots of stuff -- but it utterly chocks on these files. VLC is at least playing them -- just falling short on hitting perfect performance. So this shows there IS some tuning that can be done between iterations of SMB transfer rates.
Thank you for your time