Most of the other features that both screen and tmux include give me reason enough not to use either one. If you're just in it for the detachability, see dtach. <http://dtach.sourceforge.net/>
tmux and screen make it comfortable to manage multiple sessions. That's why I don't just use dtach. Having one session with multiple buffers/windows is easier to manage than one file for each dtach'ed program. Basically, I'd have to script my way out of dtach's bare bones session management feature set.
I don't really use tmux's or screen's split functionality, and if I did I'd probably start using http://www.brain-dump.org/projects/dvtm/. Hmm, abduco seems like dtach on stereoids and is thankfully separate from dvtm and required for detaching dvtwm sessions. Maybe I should give that a try.
Some people like split panes, though.