Is there any difference in the quality and quantity of cooling and heating from a heat pump and that from other cooling and heating systems?
No. In its cooling mode, a heat pump supplies exactly the same kind of cooling as any electric air conditioners. In its heating mode, the temperature of the air supplied by a heat pump is not as hot as the air supplied by a fossil fuel furnace, but the end result is the same: a warm, comfortable home. Air temperature from a heat pump at room outlets normally is about 100 degrees Fahrenheit compared to about 120 to 130 degrees from a fossil fuel furnace.
The heat pump warming effect thus is something like warming your bath water more gradually and uniformly by turning the hot water faucet to a moderately warm setting rather than turning the faucet all the way to maximum hot water.