This post contains status info on the 4 Kodi add-ons that support Emby playback in Kodi.
Kodi Media Source Info
There are two main ways for Kodi to display media items:
From its internal database using native c/c++ (Syncing)
As a list of ListItems generated by an add-on in Python querying an external server (Dynamic)
There are advantages and disadvantages with both of there when dealing with external sources.
From the internal DB (Syncing)
Pros
U
It is already migrated, but you need to install it from beta repository, called "Emby-next-gen"