Distro packages and to some extent Flatpaks, use shared libraries which can be updated independently of your app.

So for example, if a vulnerability is discovered in say, curl, or imagemagick, ffmpeg or whatever library an app is using: for AppImages, this won't be fixed until you update all of your AppImages. In Flatpak, it usually can be updated as part of a dependency, or distributed as a rebuild and update of the Flatpak. With distro packages, you can usually update the library itself and be done with it already.

AppImages are convenient for the user in that you can easily store them, move them, keep old versions around forever easily. It still doesn't guarantee it'll still run in distros a couple years for now, it guarantees that a given version will forever be vulnerable if any of its dependencies are because they're bundled in, it makes packages that are much much bigger than they need to be, and you have to unpack/repack them if you need library shims.

Different kinds of tradeoffs and goals, essentially. Flatpak happens to be a compromise a lot of people agree on as it provides a set of distro-agnostic libraries while also not shifting the burden entirely onto the app developers. The AppImage developer is intentionally keeping Wayland broken on AppImage because he hates it and wants to fulfil his narrative that Wayland is a broken mess that won't ever work, while Flatpak developers work hard on sandboxing and security and granular permission systems.