Thermoelectric coolboxes are the most popular electric coolboxes available on the market. Of course this means they are generally the most economical price wise. Thermoelectric coolboxes are fan driven. Therefore you will get a certain humming noise of the fan when you operate the coolbox, so bear this in mind if you are planning to sleep in the same tent/room as the coolbox. Some models have an Eco mode which slows the fan down and largely reduces the noise output of the coolbox. Check the spec on the individual models.
A Thermoelectric coolbox is a great choice if you don't want to spend a fortune but still would like a nice cold beer or glass of wine to hand to celebrate after you bang the last triumphant peg in the tent or awning at the campsite!