I agree with all the comments about the hair lying flatter!
I would also like to add:
1. easier to wash. I like the idea of water running down between cornrows. I'm afraid of getting shampoo just sits on top of a cornrows that are braided across (not sure if that makes sense)
2. "Touch-up" - For me, the side braids tend to get loose...between installs, I can redo these braids as needed without taking down my entire head (not the case with a the "s" or across pattern)
The only downfall (in my experience) if you use growth aids and getting to your scalp. Much easier with across cornrows! If you use growth aids much sure you get a bottle with a pointed end!