It would be a little different, and it might be cool if they would give the characters opposite auras to go along with their costumes: for instance, if you were using a white costume, the character would glow black. If you were using a black costume, the character would glow white. And so on.
However, I think that the characters usually just have a rainbow-colored glow around them. I've seen the characters glow red, yellow, orange, and blue all from one Smash Ball. I'm not sure they have set colors every time they are able to unleash their final smash.
However, if anybody can prove me wrong, please do so.