No, they don't have the same taste for girls... Anyway they are not related. Probably Nero was designed to look like Dante, only Nero was fused with a demon arm. They both fight demons, but the differences are:
-Nero was raised in a Vatican-like place and became a soldier, like Credo
-while Dante fought very long time ago, DMC3 is a blast from the past, remember...?
Attitude, I can see a differences.
-Nero is much like of a deviant, delinquent soldier of Credo and His Holiness, one who don't follow orders much.
-Dante, he enjoyed most of his fights, right? just press [Select].