The comparison that I?ve seen is between a heat pump and and electrical resistance heating. If you have a good source of heat, say a well with a big supply of 50 degree water, you can move that heat to your house with a heat pump (basically an air conditioner working backwards). A kilowatt of electricity may well be able to move energy from the water in the well to the air in your house at a rate of 4 or more kilowatts. The warmer the water, the more efficient the heat pump.
The same comparison doesn?t work between a fan and an air conditioner. The fan is not taking heat energy out of the air (in fact it is making the air hotter). The fan cools by creating a breeze. The A/C on the other hand is taking heat out of the air. Apples and oranges.
