Linux user here
appimage is a self-contained universal linux app... its... basically like a portable executable that contains all what it needs to run in itself, no extra files or folders
i never actually made a appimage myself but i have read that is pretty straight forward, and since is linux-universal, it will work in all linux distros
flatpak however, although it is also a universal package, it uses the flatpak repositories, and a tool to install them either through an interface or a CLI
It's great if you like to install applications from a repository with a GUI or the terminal, but I find it difficult to distribute a commercial application like pixelbasher with that method, especially since you use itch.io
so I would recommend that you try to make it as an Appimage, or just keep it as it is (as long as there aren't many problem reports, of course).
i hope this was of some help, have a nice day!
(English is not my first language btw, so if something is not well written or it's just weird, well... sorry about that)