People bring up the DmC Dante stopped a demon emperor in his tracks but they seem to have forgotten that due to DmC Vergil shutting the Hell Gate Mundus's power was drastically reduced so Mundus wasn't even at full power....in fact the Hell Gate was his power source so he had his power cut off. So Dante slowed down, punched, and defeated a drastically weakened/handicapped demon king not a demon king at his best.
Closing off the Hell Gate cut Mundus off from an infinite source of power, but he still had immense power of his own, and the entire thing about the Hell Gate was that ultimately Mundus kept his soul beyond it. Killing Kyle Rider (or any vessel he uses) has no effect on Mundus because his soul isn't in the vessel like other demons, essentially making him immortal.
Might he have less power? Yeah. But I think you're going a little too far saying he was "drastically weakened." He was still the demon who killed his way into power, without the use of the Hell Gate.
As for genetics and power born abilities....genetically Vergil's genes is better than DmC Dante's although he is a demon and angel hybrid and those are considered powerful. DMC Vergil is the son of Sparda....SPARDA!!! Generally DmC Dante's parents seemed to have been fodder or average leveled demon and angel. Sparda alone far surpasses both DmC Sparda and Eva together, the man was god leveled who took down Mundus (who is stronger than DmC Mundus at full power) and the entire demon army BY HIMSELF.
Dante and Vergil in DMC were never considered Cambions or half demons half humans they were considered the Sons of Sparda because Sparda was that OP. Having the blood of Sparda in you actually held weight and power (such as being able to power an entire demonic statue).
This is all under the assumption that Sparda (or a son of his) has more godly power than the Nephilim race. Again, this isn't some quantifiable information you can try to compare, and it just doesn't work.
And the emphasis placed on parentage is completely worthless. So demon Sparda and angel Eva weren't nearly as prominent in the legacy as they were in the classics, what does that matter? "Son of Sparda" amounts to little more than a reputation
Plus, a lot of the stuff that makes the Sons of Sparda so important isn't so much about their inherent power, and more so because their blood is the key to something that Sparda left behind, or they have something Sparda left behind, which was done to f*ck over the demons. Force Edge, the amulets, and Yamato are very prominent in this respect - they're inextricably linked to the Sons of Sparda, but only because everything (items and the twins) originated from Sparda.
The Sons of Sparda were known for their immense power, but in DmC, so are the Nephilim. Plus, Dante is still referred to as a "Son of Sparda," meaning the name still carries importance.
Think about it Vergil, Dante, and Nero took fatal-instant kill blows and wounds like a boss while full demons (Berial, Echinda, Bael, Dagon, and Beowulf) could go down easily to a simple gun shot or sword slash. Blood of Sparda.
Dante's taken hits all the same, primarily the good ol' chainsaw right to the neck. Classic DMC enemies fell with single attacks...after being beaten to a pulp in the boss battles. Even then, it's played for cool points and making the characters look all super badass.
however the biggest detail of Dante's DT is that when used on Vergil in the Vergil boss fight....Vergil isn't affected his Doppleganger is thrown into the air but he isn't affected and Dante's DT can wear out and has shown when used on Mundus in the cutscene it wore out rather quickly.
Vergil is a Nephilim, juuuuust like Dante. Of course it wouldn't affect him.
And Dante's DT didn't wear out, he got chucked into the side of a freakin' building and it knocked him silly, shutting off his DT.
Neither was Kat affected by the DT as he she was moving about just fine. So his DT does not affect time.
Conscious ability to target enemies, I'd imagine.
Buuuuuuuuut once again, there's a whole lot being said that can't be compared between the two characters.