Are you referring to the hair actually being dirty or just having a greasy look because the guy put a little Dapper Dan or V05 gel in his hair to get the bed head under control, and the result looks a little greasy compared to leaving the bed head?
I think clean, always. Some people like myself have hair that is a little unruly. In that case getting a good cut that works with your waves and curls instead of against them, or a shorter cut, might be a better solution than dousing your head with grease to keep it from sticking up.
I think clean and messy is better but from the reactions I see people get in public, greasy people who look well combed are treated less like vagrants than people sporting a cave man look.