That completely depends on local electricity costs and climate. We get about 4 months of freezing temperatures and when I did some back of the napkin math, a heat pump installation would be cheaper than gas over its lifetime, but it was only by about 10-20%, at a much higher upfront cost.

I'm not an expert so I could've made a mistake somewhere, but my calculations said that the system would have to survive for 10-15 years before it would pull ahead of a new gas boiler.