Plex mysteriously began refusing remote connections, so I couldn't share with my friend outside my home LAN. Manually port forwarding didn't solve anything, and my firewall isn't the problem. That's as far as Plex help goes...
I went to Jellyfin (plus Tailscale VPN). Some things are really nice, but others... well, it's an open-source project, and people only fix what they see as broken. So, I've tried restarting, only to lose every single customization I did. It's not worth my time to fill out their tickets and play that lottery, so I just accept the UI issues.
Then, mysteriously, Jellyfin also quit broadcasting remotely. A month later, its server wasn't even visible on my own LAN to my TV.
So I uninstalled BOTH Plex and Jellyfin, and reinstalled both. Jellyfin still doesn't connect right. And Plex works... until suddenly it doesn't, and I have to cycle through Off/On with "Allow remote connections", until it works again, mysteriously.
PRO'S OF EACH:
Plex: Much better support in TV libraries. No need for a VPN. Simpler UI.
Jellyfin: Ability to create Collections, which are basically filter-defined libraries. Without rearranging any files, you can build a Collection of Star Wars movies, or all movies directed by Scorsese, or any arbitrary bunch of media files at all, really. Optionally, you can reduce your library clutter with these Collections: a library named Science Fiction can have all of your Star Wars movies listed as a single item (that Collection). Basically, sub-libraries, but they aren't restricted to one library's contents (Star Wars might contain a documentary on "The Making Of" that isn't actually stored in Science Fiction).