I think it depends on the cut. If you are looking to switch your bangs from side to side as the spirit moves you, make sure your stylist knows that so she can cut them to blend properly on both sides. I will say that my hair definitely looks better when the front of my hair is parted on the right instead of the left. For years I had the part over my left eyebrow, but I was mostly wearing it straight then and it didn't matter. I kept that part for a couple of months after going CG, but then decided one day to part it on the other side, mostly because I had decided to let my gray grow out and I had less of a skunk stripe with the part over my right eyebrow, lol! Since then, I've realized that my hair curls in basically one direction around my head - the hair on the left side curls away from my face, and the hair on the right side curls into my face. So parting over my right eyebrow works with that pattern instead of against it, and I get good volume in the front and no wonky pieces.
I have no idea if I answered your question, but I hope that helps! :-)
Sulfate/non-water-soluble silicone free since 8/16/10
Med-coarse, normal porosity, low elasticity
Dye-free since 11/2010