Funny that you brought superman into this. I've been watching Smallville again from season 1 and now I'm somewhere in season 5 ( by the way great series
) and in that version of superman Lex starts off as a decent guy with an obsession to know the truth about Clark Kent and eventually that destroys their friendship. Anyways It's shows how best friends can become the worst enemies because of lies and secrets between them.
And what has this to do with Vergil and Dante? Well, everything! Obviously Vergil isn't telling the whole truth, and while his goals might be noble, the ways to achieve that goal might not...
Vergil might have a hidden trauma of his past even though he got to live much better childhood than Dante, DMC3 Vergil had also a trauma because he couldn't protect Eva, so that's where the lust for power comes from.
So the obsession to rule the world could very well be there hidden inside, that way he could "protect" the world by becoming a dictator, I think that's enough a reason for a fight between brothers.