Cool boxes are inefficient mine able to hold 4 cans of beer uses as much as my full size domestic fridge/freezer, great to get cool at home then keep cool in the car, but once finished it is move back to good fridge.
We have three basic fridge designs the Peltier is always DC and can be moved without a problem, the absorption fridge does not care A.C. or DC and typical uses 8 amps, it has however to be kept reasonable upright. The same with motor driven fridges, as 12 volt latter only really used on boats.
Using LED power supplies, and caravan and boat power supplies you can get 12 volt DC however the latter are often designed to have batteries attached to smooth the DC.
In the main it comes down to cost, a 12 volt compressor or inverter driven motor is likely a lot better quality, and use less power, the Peltier is cheap to buy, but expensive to run, and soon gains heat when turned off.
In the old days you could buy Peltier with transformer and rectifier built in, however EU rules will not allow an electric only fridge using mains supply under a set efficancy level, if it can also use gas then allowed, so to run a Peltier fridge from mains the dropper has to be separate not built in, if sold in EU.
