AppImage is simpler. It requires no management infrastructure, no repos, and no package manager. You can keep multiple versions of the same application around, you can store and run them on different volumes and media, and installation and removal is identical to simple file management.
Also, you can install multiple versions of an application, but you can only run one version at a time:
Note that flatpak allows to have multiple branches of an application and runtimes installed and used at the same time. However, only one version of an application can be current, meaning its exported files (for instance desktop files and icons) are visible to the host. The last installed version is made current by default, but this can manually changed with flatpak make-current.
Ok, either those are relatively new features or they're just enver promoted anywhere.
Still, what I like about AppImage is that it is just a file that I download, put it wherever I want, and run. then delete it when I don't want it anymore.
