Long story short:
Ideal:
AppleTV video server app ON
Network Disk ON
That would be where Kodi would come in - whereas Plex is entirely client/server Kodi is designed connect to a SMB or NFS share and play from there. On the AppleTV it depends on how stripped-down the promised stripped-down AppleTV version of Kodi (
https://forums.macrumors.com/threads/kodi-coming-to-apple-tv-4.1934631/) turns out to be in terms of what networks it can connect to and what video formats it can play.
The point of Plex is that either:
(a) If you don't need transcoding, run the Plex server on your network disk (a number of NASs support it)
(b) If you do need transcoding, don't use a networked disc with a feeble processor, run a home server with enough power for transcoding (you don't need a super-high-power CPU - just something with a bit more
oomph than the cheaper NAS boxes)
that also serves as your networked storage/backup. Ideal job for a second-hand Mac Mini or a cheap Linux box. You
could build a full-blown media PC and connect that directly to your TV (that's what I've got at the moment) but totally silent, small, air-cooled options that you'd happily display in your lounge are rather expensive...
...also, plex's plugins are installed on the
server so you can install what you like, whereas with Kodi you'll always be restricted to what they can get past the App Store regs.