This is actually a layered thing.One sports a red color scheme while the other sports a more cool blue-ish scheme. (Granted this could be just Japan's thing of separating heroes and villains in general with the whole "red is the heroes color" stuff)
First, you're right that the hero gets to wear red. Very common, even Power Rangers has it as a carryover with the leader being the red ranger.
Second, the Red vs Blue comes from an old folk story of the Red Oni and the Blue Oni. The Red Oni was emotional yet kind to humans and eventually accepted by them. The Blue Oni was intelligent but stoic, still he sacrificed himself to protect the Red Oni's happiness. (Vergil preventing Dante from trying to save him from falling into Hell.)