x2, or..umm, how many of us baldies have responded by now?
I'm rather light complected and lacking natural coverage on the top of my head, so I almost always run with my head covered, even on some overcast days.
Personally I don't really prefer either... I'm not a fan of running with anything on my head. However, when it will be raining or if it is super hot out I'll wear a VISOR.
In the rain it keeps most of the water out of my eyes, and on the hot days (typically in races) I tuck wet sponges in there to try to keep cool.
Headsweats visor for me as well. Used to run without hat or visor but bought the headsweat visor in hopes it would keep sweat out of my eyes. So far so good.
Big, bald Mellon means hat, all the time, and sunscreen on the head under the hat. But like others have said, if you wet that hat at water stations, it can be very cooling.