You'd get pretty much same experience, with textual splits, modeful keyboard shortcuts to access scrollback & copy/paste etc. — which I'm not saying is bad but tmux already does that. Well, I suppose over ssh it'd allow you to access remote tmux session(s) from a local tmux, so maybe allowing little more flexibility mixing panes from multiple remote hosts(?) But still pretty much similar.
The whole point of control protocol was to allow native [G]UI where each pane feels like a native standalone terminal, no?