You could argue that there is a freedom with AppImage that you are not bound to a Store. But that would not be correct, because you can self-host both snaps and flatpaks, if you really need to.
With snaps, you have more fine-grained security privileges. For example, "httpstat" [1] is a network utility to benchmark the access to a website. As a utility, it only requires access to the network. With snaps, the packager can only permit access to the network, and no access at all to the user's files or anything else.