Very happy Jellyfin user thinking of switching from Windows to Linux

[Host-in-the-Shell]

For Jellyfin, I would most certainly recommend either Debian or Ubuntu if you want something that is officially supported and directly tracked. If it's just your library, and you've enabled the setting to save all your metadata to NFO files, then a new install will read those over pulling new data. That said, remember that if you don't transfer over your databases, you will lose things like users, settings and watch history. Not sure if you can transfer them across operating systems since I've never hosted Jellyfin on Windows, though.

For your last point, if you mean in terms of raw functionality, I'd argue that it's even better specially in terms of modularity and configurability but I am very biased in favor of Linux, obviously. If we're talking in terms of simplicity and easy intuitive GUIs, then no. You will have to contend with the terminal for the most part, with your exceptions being solely the JF GUI.