Most run it on propane, some don't say its to dangerous. You could use the 12 volt dc but only when running the engine so your alternator is keeping up with the draw. It will kill and ruin your house batteries in a couple hours without aux juice. The 12 volt dc probably does the worst job of cooling your fridge. Propane first. AC second and in last place 12 volt dc. If its warm out and you don't run you propane fridge for 4 to 6 hours it would almost take a miracle to get it cold again after driving down the road for 6 hours with it off.
So to sum up. If you feel lucky run with the propane on. If you don't feel lucky run with the 12 volt. That's actually what its designed for. Just make sure to get if off 12 volt within a very short time of turning off your engine.
JMHO