Rewiring involves changing many things at the same time, so it's really difficult to determine which factors are most important. Stock headphone cables often tahe 4 wires down to 3 at the "Y", to save weight, stiffness, girth, and maybe even money. rewiring uses better materials, geometries, and gives the shared ground double the conductor material (or at least some of the above, depending on the cable).
So, design or not, the better the headphone, the more they'll benefit from better drive, and the cables can help, and real balanced circuitry can help, if done right-- i.e., true dual-diffferential. whether it makes enough of a difference or is worth the money are different issues altogether.