What is the difference between Hot Air Heating and air conditioning with burner in basement and floor vents . And Hot water heat with furnace in basement with baseboard slant coils and air conditioning in the attic. Which heats better, is more efficient, and what are the basic cost, between two. (House it is going into will have a full unfinished basement and attic and a 2112 sq. foot main floor.)

With gas forced air, you only need 1 system. With hot water, you need 2 systems, 1 for heating and 1 for cooling so that system costs more. 99% of the units installed today, at least in the Atlanta area, are gas central HVAC. There is no relation to the efficiency between them. Efficiency is by the manufacturer and varies on what you are paying for. Minimum is 80% for gas heat, I have a 92%. Gas HVAC central is simpler, 1 thermostat, 1 system.