I have had, and do have, both. Typical propane rv fridges, and I have an ARB 50 quart "cooler" with the Danfoss compressor.
It is a toss up for me but propane will run forever rain or shine.
*Propane has to be level is why I like the ARB compressor fridge.
The propane fridge is more powerful, and bigger cabinet and has separate freezer than my ARB.
*I have solar, so it is free to run as long as there is sun. 200 watts minimun, 300+ better since you will be using other battery powered items.
I can go 3 days before the two batteries are weak if rainy or too cloudy or too far north.
Does not have to be level which can be nice when stopping along the way or having to park (not camp) on a slope.
But you do have to be aware of power usage as the fridge will need most of the available power, forget running the inverter for any length of time at night (though in daytime power is abundant).
If a camper came with either one i would not stress, both are good.
If you go from house to campground and always camp on the level pads, then propane is best.
If you boondock or travel in the camper a lot parking to sightsee and want to leave fridge on then electric fridge works easier.