A thermoelectric cool box will never be as good as the other technologies. But they have there place.
I also have the Halfords box. The one which is both 240 and 12 volt. It has a long handle and wheels. In the caravan, we used it in the awning and in the sun canopy. It managed the beer the wine and the salad. There was a constant hum during the evening, but I just turned the fan down at night.
A transportable compressor box is both expensive and only has a tiny compartment. If it is to be used in addition to a fridge the thermoelectric makes most sense to me.
I have had a few over the years and the Halfords is the best VFM.
John
Whilst I have never had a 12V compressor fridge/cool box, my son-in-law has and rates it well it runs off a battery in his converted camper van.
I have had two absorption cool boxes, and used them both away when on holiday, and at home as a drinks chiller. The first was a Electrolux and worked well, but it eventually failed, the refrigerant escaped. I replaced it with a Weago of near identical construction, and it works but not as well as the original. This one keeps icing up on the evaporator just where it emerges inside the box, I suspect there is some contamination in the refrigerant system.
I also have a large well insulated Thermoelectric cooler which I have used for picnics, days out and family family celebrations when I've needed to transport chilled or warm food about in the car about 40 miles to the event . Its even pressed into service as an emergency fridge (not freezer) when a friend's fridge failed. The down side is the constant noise of the fan which is not loud but its amazing how you can notice it at night, through a closed door, down stairs in the hall.
So yes all the different technologies have their place, Its a question of working out what will bwst meet your needs.