Screen doesn't do vertical splits. That's a dealbreaker for me. Tmux does.

But tmux has another problem: very rapid scrolling in one window will make the program completely unresponsive. In the same situation, screen doesn't have this problem. I posted to the user list and the developer very quickly sent me a patch, but it didn't fix the problem for me, although it worked for the developer. Still working with the developer on this.