There are only a couple of things that a Supervised install gets you.
The first and biggest things are add-ons. Which are other apps that are easily installed from the HA interface that run in Docker containers to improve HA capabilities. But you can do everything that and add-on can do manually by installing Docker and then installing those apps in Docker. That’s what I do since I run my HA (HA Container) in Docker so Docker is already installed.
The other big thing it gets you is a back up system called Snapshots. It does make it easy to take a backup of your HA config and then restore it later if something goes wrong. But again, you don’t really need that since you can just make a backup of your config folder manually (what I do) or via an automation/sync (also what I do with Syncthing).
The negatives of running a Supervised install is that you have no control over when the supervisor updates and it has been known to break things (see the recent threads about supervisor updates and Docker-ce versions).
And since the Supervisor system is very persnickety about the environment it runs in you get an error in your system logs that you are running an unsupported installation unless things are set up exactly as the supervisor expects it to be. And if the system reports as “unhealthy” (see the aforementioned threads about the supervisor) then the supervisor is blocked from updating.
I’ve wondered this myself, too. I’m running Supervised as it was easy to just get going. However since its all setup now and configured; I see little reason to move to Core. Thanks for the info @finity