Speaking for myself: I switched from Kodi to Plex after finding that Plex requires considerably less effort to achieve greater functionality, and the differences are things that I actually like. Your mileage may vary.
As an example, let's say I want to start watching something on a tablet and finish watching it on a TV. This is something that Kodi and Plex can both do, but let's consider the details.
Kodi needs a file server and a MySQL server, while Plex needs a Plex Media Server. Thus, Kodi talks SMB/NFS + MySQL, while Plex talks HTTPS. If you want to access your stuff remotely, Kodi needs a VPN and suffers from latency, while Plex works fine with port forwarding.
Kodi needs you to configure sharing and database access on each install, usually by editing config files. Plex needs you to log in with your Plex account and point it to the Plex server(s) you want.
Kodi needs you to jailbreak, sideload, compile it yourself, or otherwise jump through hoops if you want to watch on iOS. Plex is a download from the Apple app store.
Kodi streams files to the device and plays them there. Plex does this by default, but Plex Media Server can _also_ transcode media in realtime as needed. This means Plex can stream a 20 mbps source file over the Internet to a 1 mbps cellular connection. Plex can also transparently paper over device limitations, using the server to transcode weird video codecs into something that your device can actually play instead of just failing.
Plex Pass (the for-pay thing) can also take all this a few steps further with Mobile Sync. The server transcodes e.g. a season of a TV show into a mobile-friendly format/resolution/bitrate and copies it to a mobile device. Now you can watch that stuff entirely offline, in addition to streaming whatever you want over the Internet and streaming over your LAN, while still never losing your spot in a series. Kodi… doesn't.
(My current experience with Plex DVR vs my past experience with MythTV suggests I could write something similar for the DVR functions too.)
I have plex and kodi installed on my shield. Plex requires me to setup an account to get videos from one app to another on the same device. It also failed to launch and got stuck in a few loops before I found this out. Trying to set it up just now it asked if I wanted to launch the server, but then couldn't find it. Then when manually launching it from the internal settings menu list of installed apps it said going to the next page would add permissions for storage, but just brought up an error so again I had to go into the internal settings menu list of installed apps and enable the permissions myself. I have already ended up in a situation where it said the server was there, running and connected, but showed me no library and I had to force stop and restart the server. I've also so far not been able to find basic settings like hiding the synopsis of unwatched media.
Last time I tried to set it up was on my NAS, and it consistently tried to re-encode video files which would have played just fine when streaming.
Maybe my experience is rare, but kodi has pretty simply worked and played my files without requiring me to setup anything online. My patience for managing my media has dropped drastically over time.
Speaking for myself: I switched from Kodi to Plex after finding that Plex requires considerably less effort to achieve greater functionality, and the differences are things that I actually like. Your mileage may vary.
As an example, let's say I want to start watching something on a tablet and finish watching it on a TV. This is something that Kodi and Plex can both do, but let's consider the details.
Kodi needs a file server and a MySQL server, while Plex needs a Plex Media Server. Thus, Kodi talks SMB/NFS + MySQL, while Plex talks HTTPS. If you want to access your stuff remotely, Kodi needs a VPN and suffers from latency, while Plex works fine with port forwarding.
Kodi needs you to configure sharing and database access on each install, usually by editing config files. Plex needs you to log in with your Plex account and point it to the Plex server(s) you want.
Kodi needs you to jailbreak, sideload, compile it yourself, or otherwise jump through hoops if you want to watch on iOS. Plex is a download from the Apple app store.
Kodi streams files to the device and plays them there. Plex does this by default, but Plex Media Server can _also_ transcode media in realtime as needed. This means Plex can stream a 20 mbps source file over the Internet to a 1 mbps cellular connection. Plex can also transparently paper over device limitations, using the server to transcode weird video codecs into something that your device can actually play instead of just failing.
Plex Pass (the for-pay thing) can also take all this a few steps further with Mobile Sync. The server transcodes e.g. a season of a TV show into a mobile-friendly format/resolution/bitrate and copies it to a mobile device. Now you can watch that stuff entirely offline, in addition to streaming whatever you want over the Internet and streaming over your LAN, while still never losing your spot in a series. Kodi… doesn't.
(My current experience with Plex DVR vs my past experience with MythTV suggests I could write something similar for the DVR functions too.)