Or is it the voltage settings, clock speed, and power limit that decides power draw regardless of layout?
Mostly this^
Cards with larger VRM systems are actually more efficient as more phases means less heat, more reliability, and less voltage ripple. The MOSFET's are transistors that convert PSU 12v to a GPU ready voltage, such as 1.25v. This process causes the MOSFETS to output a fair amount of heat, which is why you see passive heatsinks over the MOSFET's and typically not anything else in a GPU VRM setup. The hotter the MOSFETs become, the less the efficient they become, just like in a PSU.