They are pretty similar. Plex is more polished though. But what keeps me from using Plex is that the client likes to push content onto me that isn’t on my server. I can unpin those suggestions, but they always came back after some time, which annoyed me. I also don’t like how they handle account authorization. I shouldn’t have to use their servers to log into my own server.
Jellyfin doesn’t phone home ever, and it only ever shows my content.
All that being said, if none of that bothers you, Plex is still a really good media server.