Ok, so, Neon White is 1.1 Tons while Dante is >0.83 Tons, so the their AP and Dura are fairly even DSS is not on his standard equipment, but he probably should have access to it considering he has the two things that can form it and he knows how to do it.
One thing I'll note, is this
If they get into a gun fight, White’s got Nante beat there too, Superhuman Precision plus years of training in Marksmanship, White will shoot Nante’s bullets out the air.
Dante and Lady (Who he is pretty similar in terms of gun skills) have similar feats to those of Neon White's, their gun skills shouldn't have a gap, at least not as big as you're making it out to be. Dante's gun feats include:
he shootsing a demon while moving and when said demon is holding a hostage in his face,
shooting a lightbulb without even looking at it,
shooting Lady's foot gear while trying not to hit her,
shooting a small pipe while wall-running,
when Lady shoots a small target from very far away with a single bullet and
when Lady hits two small moving target while driving a car with a single bullet for each. Those are all pretty similar to what Neon White has. Regardless, if it does come to gun and range fighting (Improbable considering the two fighters), Neon does have the advantage as, unlike Dante, his gun don't break when he uses them, and it is very likely for Dante's gun to break, specially in DT.
In terms of actual skill with swords, they shouldn't be that far off, I didn't see anything that would make Neon White's skill as comparable to Dante but I'll give the benefit of the doubt considering it is a game and skill feats are hard to show there (If you take only gameplay, most sword fighters are bad sword fighters), and I'll also say it is useless to compare Dante's fighting style to an actual existant one, it is very unlikely anybody did any research when making said Fighting Styles and just animated things that looked cool, Dante's feats should be taken as they are, fighting a bunch of people without getting hit while fighting a more skilled fighter and
with a portion of the fight being when Dante was holding his breath, which is something that is very sleeped upon.
However, one needs to note the massive LS difference between them (249 Tons vs >18412 Tons), it is over 70x, a sword clash will easily result in Dante overpowering Neon White and either damaging him with a big slash, disarming him, or likely both. Neon doesn't look human, so Dante wouldn't have mercy on him either, so that is out of the question.
Neon White wouldn't really be able to escape Dante, they are both pretty great acrobats and Dante can fly, maintaining the close range gap is very much a given. The other NW's abilities don't seem worth noting in the battle either as I don't think they would give him any edge (If they'll start in range and NW can't really win against Dante in CqC, he won't be able to parry his bomb without his sword) and, of course, Dante's regen helps him staying in the fight for longer.
Overall, I would give this to Dante more often then not