This whole gel pack VS ice idea has me thinking, and having to look stuff up, to refresh what I learned in chemistry, back when Edison was inventing the light bulb hehe 🙂 .
First. The definition stated backwards: A calorie is the amount of heat that a gram of water can absorb that raises itself one degree Celsius.
Second: a kilogram of water can absorb 1000 calories for each degree it warms Celsius. A kilogram of water is about one US quart.
Third: When water changes state, IE from frozen solid to liquid, it absorbs 80 calories per gram, or 80,000 calories per kilogram/quart.
Fourth: Normally a domestic freezer is best set to −18 °C (0 °F) or colder
From what I have read, it seems to me that these gel packs, and frozen salt water, can not absorb more calories than a similar amount of water, (and they can't get colder than ice, but rather can only get as cold as the freezer is set at) but both, shift the temperature of the change of state, from solid to liquid to lower temperatures than regular ice.
Temperatures of change of state:
Pure water freezes at 32F/0C
Salt water freezes at (depending upon the concentration) 22F/ -5.5C
The gel packs that Max pointed to freeze at 18F/ -7.8C
Given all the above information, it seems to me that if you wanted to keep things frozen, such as in your freezer, then you would do well to use the frozen salt water, or frozen gell because their "boost" of heat absorption (temperatures of change of state) will occur below the freezing point of water. OTOH, if your goal is to keep food/drinks cold, but not frozen, such as in the refrigerator, or in a cooler, then you may be better served by using frozen water, that boosts its heat absorption when the inside temp reaches 32F ( the recommended fridge temp is 40F or lower).
I believe that the conduction of thermal energy, is greater with an increased temperature difference across the insulative barrier, in other words, the colder it is inside the fridge, the quicker it will absorb calories from the outside.
Regarding camping, and using a cooler:
Perhaps a blend of both technologies may work well. Ideally, any foods that you plan to put in the cooler, you should bring to nearly freezing in the home refrigerator first.