Ηe is mostly like DMC3 Dante, because he was made by mostly the same guys who made DMC3 Dante. After DMC1, they had a bit of problem recreating Dante's original personality (seeing as how he barely talks in DMC2) so when they found out that their DMC3 approach of Dante's personality was actually super approved by the fans, they sticked to that in their next game.
Otherwise, let's try to think of it in a more story oriented way. I'll try to have every DMC thing as canon. It's impossible to link everything if you look closely at certain facts, but if you don't mind letting some things "slide" to help the story "flow" better then read.
DMC3 Manga:
Dante is young man who has been through lots of stuff in his life. However, he has supernatural powers that no man can possibly compare to. He looks like he doesn't take life seriously, but deep down inside he is actually sad and lonely. He thinks every member of his family has been killed by demons (until he met Vergil) and doesn't have any actual care in the world. The world has given him nothing good, so all he does is try to have a good time while avoiding any serious talk.
DMC3 Game:
Dante's life and view of life changes dramatically by the involvement of Vergil, Lady and Arkham in his carefree lifestyle. He sees that even though, Vergil has had the same past as him, he is set on a goal, he is powerful, and invincible. Likewise, the weak (in comparison to Dante) human Lady is the same. In the end he realizes that some things ARE important, like family, and that since he is alive he should try his best to do what he can best in order to help the society. Which is to say, help Lady and continue his father's legacy by becoming a professional devil hunter. As a bonus he might get to meet Vergil again at some point or come face to face with the murderer of his mother, adding determination and seriousness to the young Dante.
DMC1 Novel:
Dante's life as a mercenary Devil Hunter isn't the easiest one could think of. Even though his incredible abilities allow him to dispatch any enemy with ease, there are still people who can challenge him face to face and not even blink. Dante's life has way more responsibilities than the life he led back at the DMC3 era, which help him mature and grow. He still has his cocky and taunting attitude, but knows when to stop and when to start. Some things are just to important to just laugh them off like he used to. Even though Lady is in the same line of work, it's not like they meet often, and not having any real friends amongst Enzo's mercenaries doesn't help him ease his loneliness. Those two combined probably led him into creating the password system that allows only people with serious problems to actually find him. His resolve to avenge his family is still strong.
DMC1 Game:
Dante receives the offer to finally get the jackpot. Mundus, the murderer of his mother is about to be resurrected, and thus Dante runs off to take him out. He starts off cocky as usual, though that almost cost him his life when Nelo Angelo almost defeated him and ended any possibility of him avenging his mother. Dante's "uncaring" charade finally crumbles as he strives to save Trish moments after she openly betrayed him, only because she had the form of his mother. That added with the fact that just before that he actually killed his own brother who had become a puppet of his previous self, hardens Dante. A way too serious Dante comes before Mundus and orders him to Silence, following with lots of fighting that took out Mundus. The death of Trish, didn't make Dante as happy as he thought he'd be at this victory. A ray of hope suddenly appears in these grim events when Trish is revealed to have survived, and offers Dante her alligiance as they beat Mundus and go to live together. Dante is a bit happier, and not as lonely as before. But way more serious than he was.
DMC Anime:
The ray of hope in Dante's lonely life, Trish, left him, forcing him to go solo once again. The recent events with the killing of his brother and what not, have not completely left him. Lady visits him now and then, but usually only to somehow take money from him. Patty enters his life, to brighten it with lots of smiles and even more cute stuff inside his shop. Little by little he starts regaining his old self. At the end of the anime, he let himself be crucified by the final boss, probably because, having lost his goal to avenge his family/find his brother/etc. he didn't really care anymore. Patty helps him recover from such thoughts, and even though she leaves, Trish returns shortly after that. And Lady started frequent there more, having become good friends with her as well.
DMC4 Game:
Dante still has no goal, but at least he has lots of friends. Having vanquished the most powerful demon in the world, makes HIM the most powerful demon. No threat can ever come to him, and since he has his friends around him, his mood isn't as dark anymore. His adventure in the game leads him to find that he has a relative, even though he had no clue about it in the past. He mostly cares about observing and guiding Nero, as the demons in DMC4 are no match for Nero, and Nero with Yamato full powered is no match for Dante without Dante even DTing. Thus the demons in DMC4 are absolutely nothing in front of Dante and he doesn't really take them seriously. Making him look way closer to what he was back in DMC3.
