Hello Garfield
The majority of the table top fridges as you describe use the peltier effect elements. These are semiconducting devices that by applying and electric current to the chip, they will move heat from one side of the chip to the other. Very clever devises, but in most applications, then need to have a cooling fan to strip heat away from the hot side.
In most applications I have seen (and heard) the fans are surprisingly noisy, and if used inside a caravan, it can become quite wearing to have this constant drone in the background.
The worst one I have come across was outside in and awning, but you could still hear it inside the caravan.
Technically they are limited in their ability to drop the temperature inside the fridge, and they are quite power hungry, fine if you are in a car going on a picknic but not such a good idea for the 12V system in a caravan. Some are supplied with their own dedicated 230 to 12V power packs.
I have one of these, and as I said its great for pic-nics as it has large capacity and is not too heavy, but for real and consistent cooling, I also have an Electrolux one, that uses the absorption method (like the caravan's normal fridge), and this can be used on gas 12v or mains. Its quiet and it cools better.