I got started with jellyfin and never used Plex but there's a bunch of rough edges:

• No apps on several smart tv/streaming stick stores, Vizio has an app for plex but not jellyfin so I would need to buy a new streaming device. Yes smart tvs spy on you but the alternatives people recommend either spy on you just as much or are expensive (Nvidia shield) and most of them still require side loading so it's a major obstacle for sharing with anyone else.
• Casting from the mobile app won't play at full resolution, you can get around this by using VLC as your player and casting from that but that causes it to frequently lose watch progress. Also stopping casting or playing the next episode doesn't work properly with VLC and you need to rapidly mash "back" to get into the jellyfin app again and queue up a new episode.
• The current release of Jellyfin desktop won't play audio for iptv streams, this is fixed in the dev branch but I have yet to find a build without other critical bugs so I'll likely need to wait for the next release which currently has no target date.
• The browser version has spotty controller support that stops working constantly. When it does work it lacks any way to access context menus to mark shows as watched etc. If you're using a flatpak browser to run it on steam deck or whatever, you'll have codec and passthrough issues (Chrome is the only flatpak with decent codec support).
• Others have mentioned the security issues which you can bypass by putting authentik or something in front of it but then you can only share with people using browser.