Ironworks:
The difference is that the generators with more "wires" give you more options when it comes to output voltage. I can't speak from experience about all the different options out there, but I have worked with a 12 wire, 3-phase head that could be wired for low and high voltage in both delta and star connections as well as high and low voltage in single phase. That adds up to 4 different 3-phase voltages and 2 different single phase voltages.
Best regards,
Andy Hall