Given the same mechanism for heat transfer (blowing air over a heating element, for example) gas and electricity use the same amount of energy to heat the same volume of air. Energy is measured in many different units, but generally British Thermal Units (Btu’s) for gas and kilowatt hours (KWh) for electricity.

At my house in Bellingham, I spend about 13 cents per Kwh and about $1.10 per 100,000 Btus, or one therm. I take my costs inclusive of taxes, base fees, and surcharges, so your rates may be different.
One therm has the same energy as 29.3 Kwh. But, the cost of that energy is over three times higher: $1.10 per therm versus $3.81 per Kwh (29.3Kwh * $0.13 per Kwh = $3.81). So: heat your home with gas.
But here is the kicker: one Kwh of electricity can generate more than 1 Kwh of heat. How? The most efficient gas heat delivery systems available are 98% efficient boilers for radiant heat systems. Of the energy delivered to your house, 98% is converted to heat that is usable in your house, and 2% is lost in the exhaust.
One of the most efficient electric heat delivery system available is an air source heat pump. These systems are rated in several ways, but the Heating Seasonal Performance factor (HSPF) is useful in our climate, where we heat much more than we cool. The HSPF is the theoretical seasonal output, measured in Btu’s, divided by the input, measured in watt hours. The most efficient heat pump (currently available in the US) has a HSPF of 12. That means that to get 100,000 Btu of heat, the system only has to use 8.3Kwh. Or to put it in equal terms, the system uses 8.3Kwh of energy to get 293,000 Kwh of energy. Magic? Nope. See my next post on Heat Pumps Explained.