Jellyfin gives you 100% control. You're responsible for setting up remote access. Which actually isn't that hard. Several IT and network admins of the community (myself included) hand out documentation on how to do this. Without completely ruining your security.

With Plex, some of the application communication is routed through their network. It requires an active internet connection and you must create an account with them. They have third party analytics embedded, use tracking pixels, beacons and device fingerprinting. Whatever personal data you have supplied is used to serve ads. This being their promoted content that isn't part of your library.