Can you heat your house with the AC running as a heat pump, or only with the furnace? Supposedly, "heat pump" heating is radically more energy efficient than burning gas or using resistive heat, but it doesn't work as well when the temperatures drop too low.
My mother's house has a heat pump in the reasonably large addition to her North Carolina house. It just can't keep up with very cold nights - in anything below 20F (not too usual in NC, but not too unusual, either); it runs incessantly. Those nights, she has to use the "emergency heat" setting, a space heater, or a couple fans to move heat from the gas side. The gas side is always comfy.
Perhaps the worst part is that in the rest of winter, the "heated" air blowing from the registers always feels downright cold. It doesn't blow warm enough air.
I can't speak to efficiency, though.
-jk