If you have shore power, run the fridge on 120 volts. If you don't, run it on propane.
The difference in temps you are seeing are likely related to the "power" output of the electric heater vs. the power output of the flame on propane. These are small differences and don't mean much in real world use. Want it colder? Adjust the
thermistor.
Where things really matter is when running on 12 volts. Yes, I know your fridge does not run on 12 volts, but this is an energy comparison.
A 5 gallon/20 pound tank of propane contains something like 10,000 (that's TEN THOUSAND) times as much energy as a standard group 24 marine battery that dealers are so fond of installing on RVs. If you want an exact number, determine the number of BTUs in a gallon of propane (about 95,000) and then convert BTU to kilowatts and do some math. I've done it many times, and, from memory, a 20 pound tank of propane contains the energy equivalent of 10,000 standard RV batteries. But I digress.
Lastly, the fridge uses a negligible amount of propane. Stove, oven, furnace, hot water heater all use FAR more. BUT, AS FOR THE COST OF A KILOWATT HOUR ON SHORE POWER VS. THE COST OF THE EQUIVALENT ENERGY IN A PROPANE TANK, the propane will cost more...especially since you need to drive somewhere to get the tank filled or do an exchange. And then there's the fact that you only pay for electricity at home...it's part of the site rent at an RV park.