AFAIK, Kodi is still client-based, and doesn't have the nice server component that Plex does. It's nice to have a single server handling transcoding, media management, etc. etc, and allowing the clients to be thin.
How "nice" do you want it to be? Kodi can be told to act as a UPnP server, and any UPnP client should then be able to pick up on it.
Kodi also has an optional web interface, which is primarily used to act as a remote, but I've found it can also be a thin client receiver--any media within the library can be streamed to the browser tab.
I take a slightly different approach: I netboot diskless clients with OpenELEC[0] and share my media library via a read only NFS share. It works great, since its hard to find any device (thin or not) that doesn't have enough horsepower to decode media locally.
This can be combined with a UPnP approach if there are also non-dedicated devices that need to access media.
I am running the plex client on dumb devices like tv's. That gives me a nice UI, sync of watched locations and automatic transcoding of content that the client cannot play natively.
I'd love to use Kodi with my Windows SMB shares - and I certainly can - but Amazon stubbornly hides the icon on the Fire TV interface. The added steps of going into `settings > applications > manage applications > kodi > launch` is just too much.