The one real advantage I know of is Tmux is compatible with mosh. I made the switch from screen to tmux and have noticed that there's a more active community.

There is an exhaustive list in tmux' official FAQ [1]: https://github.com/tmux/tmux/blob/fa27cbd03/FAQ#L15

Edit: I pasted the whole thing, but it's too big for comments.

Zooming panes alone is reason to upgrade imo.