Honestly, this scenario can't fully be thought out until the game is released in its entirety and we see the peak of Dante's strength by the time the game ends. For all you know, Dante could get some extreme rise in ability and power, kind of like the old Dante did in DMC3 (unlocking his Devil Trigger; among other things).
But Edward Cullen is pretty fast... I fear that the Dante we have seen up until now would not be able to beat him, at the <u>current moment</u>. If weapons were to be allowed, I do think this Dante would stand more than a good chance at beating Edward, however. Still kind of hard to come to that conclusion, though, since speed would be a factor (as already stated).
I feel kind of bad posting here, since it confirms having seen the first two films, but...from what I've seen, I'd say it's fairly close.
It's worth noting that the problem with Twilight vampires isn't that they're "wussy", it's that they're stupidly overpowered in a badly written way. In addition to each one getting a super power of some sort, they all have super speed of some sort, and the only way to kill one is to rip it to pieces and set fire to the remains; the sparkly part is apparently because of some poorly thought-out extension of the fact that their bodies are literally as durable as diamonds.
That said, while Edward's highly dangerous by human standards, he's not actually much of a fighter, even in-universe. Mind reading, super speed and durability are definitely advantages, but I don't think he has the skill to use them.
Funny as hell, it was the most horrible thing I could imagine...