I really meant to respond to this sooner, but consider this:
DmC Dante's swordplay is not refined, technical or pretty like Classic Dante's. His axe looks even less focused; as if he just lobs it in the direction of the enemy to deal damage, not using the weighty weapon effectively.
But his scythe is markedly different. He seems very used to twirling the scythe around and generally being fancy (he's even done Roulette Spin with it, I think) while his footwork alternates between dance-like and perfectly controlled.
I think the angel stance is his playful, showy one while devil stance is just meant for power. That's just a theory anyways.