yea it's all kinda according to a storyline,
DMC 3: Dante jus got a place for his demon slaying business and thus, we assume tht he still carrys a grudge against all demons who slayed his mother n believed his brother, vergil to be dead but is not.
DMC 1: Dante has grown a bit but stills wants to find answers why his mother was killed n a woman called Trish seems to have the answers.
DMC 2: Dante has matured, and typically demon army rises up, threatens the world and dantes saves it