Amp has an internal clipboard that it synchronizes to an external/native equivalent, if available. You'd still be able to copy/paste within a single Amp process, but you would lose the ability to do the same between separate processes.

Right, so in the context of this discussion, tmux panes are not a good substitute for vim windows, since you wouldn't be able to copy-paste between them unless what you were copying fit in a single pane-full.

Yes, that's correct. :)

In that scenario, I would compromise by opening both files in the same Amp process and switch between them, but that's not the same as seeing both at the same time.