Round 1: Who's a better marksman
Round 2: They fight
Fight takes place on top of Temen-ni-gru
R1: As far as I know, Vash.
R2: Dante stomps. The only thing Vash has going for him is his massive destructive Angel Arm and black hole hax, both of which can be countered via time stop and higher speed/reflexes. From then, Dante shoots him with his own gun.
Dante has the clear advantage here in terms of just having better feats and skills. Plus he's nigh on invincible, he's taken a giant sword through the chest and still continued casually having a conversation before taking it out. Add time control, hypersonic movements/reactions and you can see Vash just doesn't stand a chance.
And this is all pre-devil trigger.
Dante has a advantage here:
The Quicksilver Style is a time-controlling style appearing in Devil May Cry 3 which is obtained from Geryon the Timesteed. It allows Dante to move at lightning quick speeds relative to enemies and the environment, thus allowing him to experiment with different tactics and combos.
Send out a dimensional time-rift wave that slows down your enemies while giving you ultra-high speed.