[rainsford]

I don't have direct comparative cost experience, but the reason heat pumps are so efficient is that while they do indeed have to run a fairly energy intensive compressor, that compressor allows them to get heat energy for free from the outside. By using the compressor to make the outside refrigerant very cold, it absorbs heat from the outside air (for air source heat pumps) even if it's cold outside. That absorbed heat energy required expending energy to run the compressor, but it ends up allowing the system to absorb several times more heat energy from the outside air. This marginally cools down the outside air, but that gets heated back up again by the sun. Arguably making heat pumps solar powered.