I don't think it would affect efficiency much... Watts consumed is watts consumed. 12V @ 4 amps is the same watts as 24V @ 2 amps.
Where you might gain a little is through a lower percentage of voltage drop in the wiring (power lost as heat), however thicker wiring would counteract that.
I would say to run it on whatever voltage your vehicle provides.
I'm not familiar with a 'Mog's electrical, but if it is a 24V system, then that's what you want to run it on. Efforts to convert the voltage from one to the other would result in additional losses (or a severe battery imbalance in the case of trying to run it off one battery of a 24V two-batt system)