To be fair Dante is still cocky and so sure of himself that he reacts as if he doesn't even try seriously against the DMCC2 enemies. To me it looks as if he's extremely bored, yet still has to do it, so he does.
A perfect example for that is the battle against Trismagia in which he says: "Don't talk, just die." Implying that he's already heard that you're-the-son-of-Sparda crap millions of times already and doesn't really care to go through with them again. His power is already on a whole other level, beating the Despair Embodied without even transforming in the cut-scene, and being totally cool while doing it.
In a way he is still Dante, he is still sure of himself and overconfident, but it seems the DMC2 plot/enemies aren't enough to satisfy him and adapt a more this-is-fun attitude.
And to be honest who can blame him.
Thank god that this same Dante plays in SMT3: Nocturne. And he is more than alright there character-wise. For me after the DMC2, Dante traveled to many dimensions to kill demons - as I take every DMC-thing as canon, as much as I can - and by kill demons I mean "have fun" as well. After all according to him in DMC3 "this is what he lives for" XD