You know, 醒 means 'wake up, regain consciousness'. If you just say 他醒了, probably he woke up from sleep, but also could be 'woke up from drunkenness or coma'. If you add 睡 in it, that only means from sleep, not for other situations.
So when you just want to say 'wake up from sleep', either way is okay to use. We say there is no difference between the two in that situation.