Where each system genuinely wins. Nothing here is universal, electricity and gas prices in your area decide most of it.
Heat pump
Gas furnace + AC
Equipment needed
One system, heating and cooling
Two systems to buy and maintain
Efficiency
250–400% (COP 2.5–4)
80–98% AFUE, never above 100%
Running cost
Usually lower, unless your electricity is expensive and your gas is cheap
Can win where gas is very cheap
Comfort feel
Long, steady cycles of ~95°F air; even temperatures
Short blasts of 130°F air; warmer then cooler
Very cold weather
Cold-climate models hold capacity to –5°F; below that, backup heat
Unaffected by outdoor temperature
Combustion & venting
None, no flue, no gas line, no CO risk
Flue, gas line, annual safety check
Federal tax credit
Qualifies for the 25C credit
Smaller credit, high-efficiency models only