Totally different software solutions aimed at different users, and many people use both.
Plex is a Server software that handles media management, libraries, users, etc etc… and a range of player apps that have a somewhat beginner friendly layout requiring little to no setup
Personally, I run a large Plex server that provides content for my family across dozens of mixed devices in home and out of home, different users have access to different libraries and have different preferences. If needed it will automatically transcode content for remote users out of the home to fit my upload bandwidth and their available speed if they are on mobile. it keeps track of watched content and position for all users so they can move between devices seamlessly.
Kodi is an extensible media player frontend, it can play files from a remote server or NAS but there is no server management, it is just doing basic file access. there are addons for many common services and media sources but there is no user management, no transcoding, no sharing content with other clients etc etc. Having multiple kodi installs on multiple players requires each client to be configured more or less from scratch and no easy way to have multiple setups for different users with their own preferences, libraries and/or content restrictions. It is extremely powerful and configurable and has strong format support.
I have Kodi installed on one of my Nvidia Shield Pros but only use it for playback of surround music files (support for 5.1 flac on plex seems to be limited to audio within video containers for some reason) I find the interface (and all the skins I tried) extremely clunky for use as a music player, the way the remote works within the player itself is unintuitive and makes for an annoying experience restarting the track when you just want to move the playback a few seconds, a bit unfair of course as that isn’t what it was made for but that’s just my experience.