Triple fuel fridges are most efficient on mains power.
In fact electric heaters are about as close to 100% efficient as you can get.
With electricity, the power can easily be controlled by a simple bimetalic temperature sensitive switch. When the fridge is cooled, the power turns off completely, meaning power is only used when its needed.
The heating element can be placed exactly where its needed in the refrigeration system and does not need a flue to remove products of combustion as there are no products.
When a gas flame is used, the burner needs a flue to allow products of combustion to escape. Without it the burner simply could not work. The flue needs some energy to drive the combustion, which it gets from the fuel being used. That energy is an inefficiency. flame may not be optionally placed to deliver heat to the refrigeration system- -another inefficiency. Thirdly practically you cannot burn a hydrocarbon fuel without producing some emissions. They are a third inefficiency.
By the fact that this thread is discussing "Safefill" cylinders and other suppliers have also been mentioned proves that Calor do not have a monopoly.
Whilst some more modern fridges do turn off the gas when cooling is not needed, older ones continue to burn the same flame regardless. That is another potential inefficiency.
Caravan fridges are only designed to use 12V when being towed, so are not worth considering for long term power.