Tmux is sweet as heck
me.veekun.com
me.veekun.com
For example, screen has zmodem and lua scripting built-in. Screen can ask for a password when someone attempts to attach to a detached screen session. There are probably other advantages that screen has over tmux as well. I haven't done an exhaustive analysis of the differences between the two. But I know screen has a boatload of options and features, and wouldn't be at all surprised if there are a number of other areas in which it shines.
That said, I switched from screen to tmux some years ago, and am quite happy with tmux, as it mostly suits my needs. But it would be nice if it was more scriptable.