Flathub aims to be the place to get and distribute apps for Linux. It is powered by Flatpak which allows Flathub apps to run on almost any Linux distribution.
How does it stack up against traditional package management and others like AUR and Nix?
I definitely prefer it over Snaps or appimages. Straight-forward to update, and Flatseal provides a nice GUI to control permissions (if needed). Themes may not work properly, but whatever, not a big deal for me.
The distro's repo is always my go-to. If it's not available there, then flatpak, and I'll use appimage under duress. If that doesn't work, I'll figure out a different solution.
Yeah I'm not a huge fan of Appimages because I don't like that to update it you usually have to go find and download the file again, instead of just getting it from a repository. They feel too Windows-y to me in that way.