tmux and screen both have upsides and downsides for pair programming. Ones that I know of:
1. screen requires itself to be setuid root for session sharing. This is security issue to say the least. The frustrating part of this is that screen explicitly checks that that uid == 0. This means that, even if you can iron out all of the permissions issues between you and your partner without needing root access, screen will only accept suid root as the solution.
2. When you are screen sharing in tmux, the configuration used is the configuration of the person hosting the session. This can suck if you have a lot of non-standard bindings, because it forces the person you're pairing with to know them too. screen allows you to both use your own configurations while being connected to the same session.