A gas furnace burns fuel; an electric-resistance furnace uses heating elements. Both need a properly sized distribution system. An electric heat pump is a different technology and should not be grouped with resistance heat when comparing operating cost.
Capacity, clearances, controls and service costs are model- and house-specific; fuel type alone does not establish them.
Compare heating cost on the same basis
Get the home’s estimated heating requirement, the proposed equipment efficiency and your actual utility tariff. Compare the cost of delivered heat rather than gas and electricity prices printed in different units. Fixed service charges may also matter if a fuel connection would otherwise be removed or added.
ENERGY STAR explains AFUE as fuel energy converted to space heat under the rating method. It does not include every distribution or household cost. To earn the label, ENERGY STAR requires gas furnaces to reach 97% AFUE or higher in the U.S. North and 95% in the U.S. South, and oil furnaces 87%. The contractor should state the assumptions behind an annual-cost estimate; an unexplained national dollar figure is not a prediction for your house.
Installation can change the answer
For gas, verify the fuel supply, venting, combustion-air arrangement and condensate requirements of the selected furnace. DOE’s direct-vent guidance explains sealed combustion, which separates combustion air from the occupied space.
For resistance heat, have the electrical service, load calculation, circuits and required clearances assessed. Empty breaker spaces alone do not prove sufficient service capacity. Neither type should be selected solely because the old cabinet fits the opening.
Both need suitable ducts, returns, airflow and controls. A heating problem caused by poor distribution can remain after a fuel change.
Include a heat pump
DOE’s DOE: how heat pumps work explains why moving heat can use less electricity than producing it with resistance elements. A cold-climate proposal still needs capacity, temperature performance, defrost and backup-heat planning. Compare a complete design rather than assuming a heat pump cannot work because winters are cold. ENERGY STAR tests certified air-source heat pumps for low-temperature performance down to 5°F and suggests a backup heat source for colder weather. Ask for the heat pump’s output at your local winter design temperature and how supplemental heat is controlled.
A heat pump also cools, so its quote can replace both the furnace and the central AC; a furnace quote needs separate cooling if the home has AC. A dual-fuel arrangement, which ENERGY STAR describes as heating with either the heat pump or a gas or oil furnace and using each based on cost and environmental benefit, may also be appropriate. The right comparison includes installed cost, local tariffs, control settings and the share of demand each component is expected to serve.
Maintenance and safety
Follow the actual manual for filter and homeowner maintenance. Gas equipment adds combustion and venting checks; electric equipment still has high-current components and safety controls. Do not open energized compartments, bypass controls or treat combustion smells and CO alarms as normal behavior.
Ask for local service availability and written warranty terms for the identified models. There is no failure-rate evidence here that establishes a universal repair-cost winner.
Decision
Request comparable proposals for the same calculated heat load. Compare total installation and operating needs, including a suitable heat-pump option. An existing gas connection is one consideration, not a requirement to buy another gas furnace.