I've honestly not found a single feature in tmux which I need which isn't already covered (and imprinted in finger-memory) by GNU screen.
On the flip side, I'd ask: What reason is there for a seasoned GNU screen user to bother switching from something proven, and which works?
I switched to tmux when I needed to launch a lot of simultaneous jobs, categorized in three sessions (starting in "active", moving to "success" or "fail" when finished). I couldn't achieve it in screen at the time. The CLI interface of tmux is not very intuitive and I think somewhat inconsistent (maybe a bit like git?), but at least I could achieve what I wanted without major compromises.
After a quick google search my impression is that running a shell command in a particular GNU screen window is still painful.
Sure. And let's go full circle while we're at it: GNU screen supports connecting directly to a serial device :)
Last I checked tmux doesn't.