Something people fail to see for some reason in this series is that Dante is pretty much a completely different character in every single game.
In DMC1 he is a wisecracker but his mission is one of revenge and hes more driven by that than having fun and shit.
DMC2 Dante is a silent stoic who only speaks when necessary. This Dante acts like he has many many years of experience under his belt and prefers to just focus on the mission.
DMC3 Dante is an inexperienced shit talker who loves to just have fun and show off. He doesn't give a damn about anyone but himself and having fun. He refers to the blood feud he and his brother have as a party.
DMC4 Dante is the most like another Dante in the series, DMC3 Dante, but his personality differs in a few key areas. He still is a shit talker and loves to have fun, but now he cares for others and their well being. He is so powerful now that he is supremely confident in himself. Despite this overwhelming power, he doesn't let it change him and he prefers to act like your goofy uncle than a grim warrior.
DmC Dante starts out kind of like a more realistic DMC3 Dante, though much more vulgar and such. He matures at the end, same with DMC3 Dante, but like most people say, first impressions are very important.