You literally didn't pay attention to either DMC1 or DMC3. Dante's arc in DMC3 is a good example of his character. He hates his demon side and his father due to his mom dying. He's only able to surpass Vergil, who idealizes his father and demon side, by accepting his demonic half. However, unlike his brother, Dante doesn't throw away his humanity or see it as a weakness. The family drama's mirrored by Lady and her Dad. And when he sees this, and how she's taking responsibilty for her family's actions, Dante outright tells her "I know what's really important." So he goes from not caring and just wanting to have fun, to honestly wanting to save his brother from himself. By accepting both halves of himself, he reaches his true power. How is his mom dying and his brother being corrupt not on the same level as Bayo and Kratos?
I would honestly argue Dante's a decidedly deeper character than both. Bayo's basically just Dante, but less games to flesh out the character. So how you see value in her and not him is particularly confusing.
Most cutscenes show you this. Just watch the compilations on Youtube or something. Scenes like him trusting Nero with the Yamato, and even the cheesy "Fill Your Dark Soul With LiiiiIIIIGHT" Kind of show the type of guy Dante really is.