JF becomes better or Plex becomes worse

Both will happen.

Besides.

some subtitles work on one, but not the other and vise versa

For me it has worked everywhere. All of my media is in .mkv so it already contains the subtitles. It works in all browsers clients, Desktop clients, TV and Mobile clients. Works in VLC and MPV as well on desktop, TV and Mobile. Works with Kodi as well. Works on same network (via both host IP and reverse proxy) as well as remotely via Pangolin.

So you can try putting everything in one MKV Container or maybe change the subtitle formats (if that's a thing).