All of them are great.
DMC1 Dante is cool, easy-going and ready to return to you exactly what you threw at him. Be it an attack or just words.
Despite seeming a good-for-nothing guy who rests his legs on top of his desk, he actually takes his job quite seriously. His exploits have made him somewhat popular around the neighborhood (according to what Enzo says in the DMC1 manual) not only for his extraordinary strength but for his eccentric taste in choosing assignments as well. Instead for going after money he prefers choosing to deal with anything related with unexplained phenomena, a typical modern-age ghost buster. Further proof of his serious-but-behind-the-scenes nature is that he has deviced a Password so that only people who really need his services might reach him. DMC4 Dante (I mention him instead of DMC3 Dante because he is older and closer to DMC1 Dante)seems like a big kid. He is constantly nagged by both Lady and Trish, while he shows little interest in what goes on around him. He is pretty good guy all in all, listening to Credo's last wish, guiding Nero and all that, but he's as much chaotic as he was back in DMC3. He threw himself into a battle from the beginning of the game, then disappeared for most of it doing...nothing? It's like he went there, saw Nero and thought..oh well, let's let him take care of all this mess. I'll go for a walk. Damn Nero is angry. As an adult I must make him realize the importance of being calm. *beats up Nero*. Oh..come on kid, is that all you've got? Oh no he got caught by a giant statue. Okay..instead of battling it, I'll go smah the hellgates. He'll probably be okay by the time I'm back. *finishes*. Ok kid, here's your sword back *throws Yamato* now end this game. If it takes you less than 3 missions I'm gonna let you keep it. I don't really care for it.
In DMC1 we get to see a glimpse of his inquisite nature as well. He has a personal comment to offer for every statue, bookcase, etc. which makes him difer from the other versions of him in the other three games, who throw themselves into any chaotic situation without any care in the world. Both DMC3 Dante who went after Vergil like nothing major happened and DMC4 Dante who let Trish give Sparda to the Order while he was pretty much fooling around throughout the whole game until Nero got himself caught.
DMC1 Dante's taunts and smartass phrases are only a facade of his real self. We can see that when he often shows compassion (Griffon's last battle), admiration (Nelo Angelo's last battle), and other strong emotions even to his enemies. He knows when the situation is ok for smartass talk and when he should be serious.DMC3 Dante in comparison, fools around with everyone no matter the situation(example: the battle against Beowulf. It's one of the battles he was close to getting beaten just because he wasn't taking the fight seriously, only managing to cut Beowulf's remaining eye, but at the cost of being shoved into the floor. Since DMC3 Dante was pretty much on Vergil's level at this point since their battle shortly after that had no victor, he could whipe the floor with Beowulf's hide. However he was as careless and "ready for party" as ever), with the exception of the battles against Vergil - possibly because if he didn't take those battles seriously he'd have no possibility of winning. I know that he supposedly is young and all, but looking at Vergil's character, DMC3 Dante's age is no excuse.
DMC1 Dante's shop is also my favorite. I don't know how and why, but the way it is depicted in DMC1 (even though supposedly it's always the same) really gives me the creeps while also awakening an I-want-to-see-this-place-from-close feeling. In the other DMC games, the shop somehow looks less threatening and more accesible. I could easily imagine its existence in someplace like Disneyland (Capcomland?) as an attraction. I'm not saying it's not awesome, I'm saying that in DMC1 it's both creepy and awesome. Perfect HQ for a guy who kills hellish monsters from another world.
Also DMC1 Dante doesn't seem to have any problems with the rest of his family. I don't know where the "Father? I don't have a father..." etc stuff that DMC3 Dante says come from. His "rivalry" with Vergil, though understandable and well-liked is pretty childish as well. At the beginning of the game he just wants to stop Vergil because...that will annoy Vergil or something. And I didn't get why Vergil didn't go to take the amulet himself right from the beginning. In the first two missions it is implied that somehow Arkham or Vergil or both, control the lesser devils, senting them at Dante's shop - probably to steal the amulet. After that we see that Vergil kills devils as much as Lady or Dante do. I think something was missed there director. Making not only DMC3 Dante but Vergil as well looking a bit ridicilous. Somehow DMC3 Dante had to go through all this (DMC3 story) in order to realize the importance of family. And he understood that from a crazy girl that shoots everyone without warning and came here to destroy her father. O..kay..? Vergil feels more understanding of the whole family bussiness - lecturing Dante about might didn't seem to me like he was being full of it. He probably wanted to make Dante understand that with power you can do almost everything and protect everyone. While without it, even your self is lost. Of course if Vergil left some girl pregnant with Nero a few years earlier, that takes away every qualification he might have had of the "family" term.
DMC2 Dante is actually super cool. Only he is like a totally different character. If he had black hair and his coat was not red, we'd never understand he was actually Dante.
Anyway, despite the ranting I love everyone. Maybe DMC1 Dante just a biiit more. Then comes DMC4 Dante. He is also awesome<3