Compressor refrigerators work faster and are more energy efficient, as they are just small versions of the household fridge.
12v/ propane models work with very little external power, but take longer to cool. Ours can run for 3-4 days on the single battery on the camper, and of course propane. They can run for a WHILE on a 30 pound cylinder. They operate by making heat and, physics and stuff, doesn't matter. They just make heat to make cold.
That said, I've never had a problem with any of the 12v/LP refrigerators in any of our campers. Though, there is more "stuff" to fail.
For me, the ability to have my fridge cold while driving down the road is priceless, and would never NOT have a 12v/LP RV fridge. We also do a lot of "dry" camping where we are on generator power when needed, shut the generator down when not needed. We still have a cold fridge because it switches over to propane/battery. We do have a "mini fridge" in the outdoor kitchen in our new camper though, and it is just a standard AC power only. It is good for drinks and such that don't have to stay cold to avoid going sour, like your food.
ETA: If the fridge is 120v AC with propane, I would go 12v DC 87,000%. There are no advantages that I can see being 120v AC dual fuel fridge, and you loose the ability to run on battery power.