Aman Khapde 27 y.
I think a being handsome has to do with a man's physical features, like his face and his build, whereas being sexy has to do with attitude and personality.
For example, Donald Draper from Mad Men is very handsome. But for me he's not really sexy because he's not mischievous enough. A man has to be at least a little bit mischievous to be sexy ;-)