The titles and lyrics of their respective themes all allude to their acceptance of their demon heritage.
-Dante already accepts that he’s half human and half demon, but he probably doesn’t even care, all he really wants is some pizza and to make a stable living from his job (speaking of which, where does he even live?).
-Nero has also accepted his quarter demon heritage, but the lyrics almost implies he’s getting obsessed with it. “This demon inside has ahold of me / Clenching its power - trying to break free / Gotta let it out - gotta let it out.” Like father, like son, their demon blood is pretty strong.
-Vergil accepts his demon heritage, but to the extreme. His theme title, “Bury the Light,” alludes to him burying his humanity. Vergil is so obsessed with obtaining more power, we see him resort to extreme measures, as seen with him “purifying” himself by splitting himself into his demon and human halves with the Yamato.
You can even hear his obsession in the lyrics if you listen hard enough. “My Family crest is a Demon of Death.” Even after going through all that character development through his human half, he still wants more power. Bless him