This data probably isn't published separately, but one efficiency parameter is the compressor efficiency. Another is the insulation value. Some of the newer fridges are much more insulating than the ones of a decade ago. If there's any way to find out that information, even just from reviews, it's probably worth knowing.
I like the idea of using a chest freezer as a fridge simply for the efficiency advantages.
If you're running it off
solar, or any other intermittent source, or you want it to perform better in a power outage, I figure the most practical and least expensive form of energy storage is ice (as compared to say batteries). To implement this, ideally there would be physical contact in order to form a conduction path between the evaporator coils and the ice/water storage, (although it's not strictly necessary). Supposing that the rest of the fridge was cooled by convection, then that would be the bottleneck for heat transfer. If the design worked out right, then it might be possible to get away with a single temperature controller cooling the air in the fridge to nominally 40 deg.F ( 5 deg.C). Presumably then the evaporator would have to pull heat out of the ice/water before pulling heat out of the air, since there would be a lower thermal-resistance to the ice/water than to the air. This might mean the ice/water temperature would have to drop down to freezing just to cool the air in the fridge to say 40 deg.F. That might be a way to have below-freezing thermal storage and at the same time an above-freezing fridge while using just a single thermostat.
If the food or drinks were getting too warm or freezing, then maybe the ratio of evaporator surface area touching the air versus area touching the ice/water could be adjusted until the balance was right. Or more simply, I suppose the thermal storage could be placed in the colder spots, and the food & drink in the warmer spots. Then just adjust these positions and the thermostat setting until the ice packs tend to freeze but the food & drink doesn't.