Jellyfin Is completely open source, fully self-hosted, and free. With Plex the software still has to phone home to a central server for authentication and some features are locked behind a paywall.
No streaming software is going to find movies for you (without paying for content they've licensed) because that would be a sure fire way to get the project taken down for copyright violation.
While I don't have much experience with Plex, I can say that it's really not hard to set up Jellyfin for streaming across the internet.
I'm running a docker container using the linuxserver.io image and all I had to do was forward the HTTP/S ports. I will grant that when a third party has to make an easy-to-use container for a service, there's a problem to address... but if I remember correctly, Jellyfin is easier to set up on bare metal where it can use uPnP.