I’ve yet to have the first be as smooth an experience as just using the native package manager. Be it some app misbehaving or needing manual permissions tweaking, or a missing/inexistent GTK theme, amongst other issues.
Distrobox/containers are however pretty cool indeed. I don’t use Distrobox myself, but there are many things in my shell’s RC that’s just a wrapper alias/function around some docker image already.
Limitations surrounding theming (no way to force a theme and flatpak basically just doing a best effort to use the right one, theme needs to be specifically repackaged for the platform, etc) has nothing to do with the packager and everything to do with Flatpak’s sandbox. Same for permissions: running something like an IDE or anything that integrates with other software over Flatpak is just a pain in the ass due to the sandboxed nature.