I'll fill in what I can -
>- how easy is it to administer for clients outside of my network or possibly even outside my country?
Jellyfin is just the software, not a hosted solution. I use a simple server/seedbox, with sane configs (good providers have automated this), which results in a secure public-facing admin console with a username/password. They have basic user management features to include other users in your server.
> - how good is the app support? I transcode all of my media to AAC and h264 for compatibility
Jellyfin has a broad ecosystem of apps on a bunch of platforms, each with their pros and cons. I recommend poking around. When figuring my setup out, I downloaded 3 or 4 different Android apps to pick the one I liked (support for multiple servers which isn't a given in all the apps)
> -what about for streaming music? I really like Plex amp
IMO Plex has always been substandard here since they hoisted the music interface into the same one they use for everything else, so it's really lacking in filters/administration features I depend on. That said Jellyfin supports music and has the same simple feature set.
> - what do you like the most about jellyfin
It's free and untethered to a company's whims. It also does a lot less of the social/DVR stuff that I have no interest in.
>- what do you miss most about Plex?
Their app experience was a bit more premium, and their support for multiple servers is better than Jellyfin since they own the servers/hosting to do it. I also really used to enjoy the 'remote' functionality where I could skip episodes by clicking next on the Plex app in my phone. This hasn't worked for a few years for me despite heavy troubleshooting.