My preference is AppImage if available otherwise I go with the distro default and as last resort 'sudo apt install'.
AppImage works great because I run one main host with numerous VMs serving different functions. I locate the AppImage on one disk shared to all VMs. The one install and execute from any VM instance is the big sell point for me.
I'm using Pop!_OS 24.04 mostly and it defaults to using either Flatpak or 'sudo apt install'. An initial pain point for me with Flatpak is it stores the binaries in a unique location. To execute any flatpak installed binary for automation purpose, one has to execute 'flatpak run <appname>'.
I think the missed opportunity by most developers is not generating an AppImage for their application. It might just be me but I don't like applications pooping all over my hard disk.