because they require more access to the system
afaik, you can allow more system access to flatpaks
Ubuntu runs a virtual filesystem in order to allow its Snap Firefox to access the Dictionary that lives "outside" its sandboxing
i believe flatpak also does that, you can specify some paths from the host to be available to the flatpak
i can understand that, but flatpaks are easier to upgrade and automatically integrated into your package manager, which (i believe) isn't as straight forward for appimages. also there's one major repo where you can find most apps (flathub) making app-hunting less daunting i feel like.
also, once your app is installed, it's always in your system menu, so that doesn't change much in the long run
can't you carry over flatpaks as well? you can probably copy /var/lib/flatpak or wherever they store their stuff from one system to another, or failing that, save all the app IDs you have installed, and re-install them onto your new system, backing up ~/.var to keep all your data!