If you do a shared session tmux has one feature that was a big deal for me when comparing to screen. tmux will use the intersection of terminal resolutions of users in the session, whereas screen will use the resolution set by the creator of the session, which easily results in a too-large and unusable display for the other user.
Personally I switched because I could read tmux config as opposed to screen's, and tmux is shell friendly. I use ubuntu and the default screen there has vertical panes for a long time, so that doesn't factor in.
tmux being shell-friendly means I write one shell script for each project, and if I restart the system for some reason, I open the terminal and run tmux-foo. tmux-foo creates a session, cds to project root and create multiple windows, opens vim in one, rails s in another, logs in another, rails console, dbconsole etc etc.
If you are curious, pick a config which gives you screen like keybindings(tmux uses c-b; I swore to screen long back I would use c-a) and try it for some time. As far as user experience goes, you have everything you had in screen with some added benefits(no, it isn't bmw)
...except for serial communication. Because I connect to various hardware UART devices all day, I need serial communication. I hate minicom and most of the other serial comm programs don't have the features I need.
Since I'm already using screen as my serial communication software, I go ahead and use it for terminal multiplexing and session management as well.
Yeah if it's pretty much the same, then I don't really care to change. I'm used to screen and happy with its functionality. Vertical splits aren't game-changing enough for me to learn a whole new app.
I love tmux, but it's crazy that they went to all the trouble of rebuilding screen without fixing one of the most glaring flaws to a newcomer: the guaranteed-to-conflict default key binding.
Screen is nice, sure, but tmux has a couple of tricks up its sleeve.
And if your net connection is a little shaky, tmux can save your sanity (whereas screen just hangs there)