I don't know about snap but from what I have seen of flatpak, it allows for different versions of the same package to be installed, not many package managers are supporting that currently. (Nix and Guix being some notable exceptions, and those should be able to re-use some of the sandboxing bits from flatpak if they need to) Of course, that is one of the main benefits to building this on top of filesystem overlays, and why it requires a different approach from a traditional package manager, i.e. it's not just a duplication.
Edit: Live migration actually does work for containers, take a look at CRIU. (I don't know the current status of this being integrated in Docker) I never even saw this as being opposing technology anyway, for example if you need to you could migrate a container in or out of a VM.