First off, due to the physics of their operating mechanism, heat pumps can only provide heat down to a certain temperature. Some can operate at temperatures as

First off, due to the physics of their operating mechanism, heat pumps can only provide heat down to a certain temperature. Some can operate at temperatures as low as 0°F (albeit inefficiently) but even for those models, the efficient minimum temperature is still around 25°F. So if you live in a place that gets colder than that, and you insist on electric heat, you would likely need to go for resistive heating (like wall heaters). But resistive heating is not great, in part because it dries out the air so much. In terms of cost, I happen to have both a high efficiency gas furnace and a high efficiency electric heat pump in a home with great insulation, and have been able to experiment with how they compare for heating the home. We don't get winters that go below 25°F, but gas heating is FAR cheaper (I estimate less than half the cost). We personally feel the air quality is better with gas heating as well, although this might be subjective.