Cost is going to vary greatly on the electricity and gas prices in your area, so it's hard to give a definitive answer there.

With regards to energy efficiency, my understanding is that heat pumps can be up to 400% (300% typical), which is naively much better than gas which is at most 90% efficient (70-80% typical). This doesn't take into account the extra innefficiency of generating the electricity in the first place, but a quick google tells me coal plants are typically 33% efficient, with combined cycle gas plants being typically being 50% efficient. Even at those levels, heat pumps still look to be coming out ahead to me. And that's not even taking into the possibility of green energy generation through renewables or nuclear.