Drewster, I dont know whether there's a structural advantage or not. I'm guessing it's give and take... a compromise of sorts. Going from thin and flat to round makes a spring or lever stiffer and stronger, or equally as strong with less material, but going from round to thin and flat means it can bend farther without breaking. Most of my bows would be defined as flatbows, but are of such a cross-section as to perhaps share some structural qualities of each of the above.
I make them that way mostly because of how they look, but there are a few advantages and preferences when it comes to tool application, tillering techniques, and how they're better suited to some of the bows I prefer, like really snakey or odd shaped osage bows.