It depends, there are no hard rules. I have a preference for the native package manager with pacman and repository of my distribution. I also would like to use AUR more often, but it depends who is maintaining that package. It also depends if there is a Flatpak available. Some AppImages have an auto update for itself, so I download it only once and use the applications own update functionality manually.
The good thing about AppImages are that they usually don’t require super user privileges to install (in other words use) them and I can also archive them very easily.
A perfect example when to use AWK.