Specifically, as I recall from the Technology Connections video on space heaters, transmission losses mean that electric heating is less energy-efficient than burning the gas yourself, since most power comes from gas and coal. Solar doesn't work well in winter and at night (without energy storage anyway), and wind isn't reliable.

If you lived next to nuclear power though, electrical heating would beat gas. Between those two it's a mix. So these sorts of decisions should be based on whether your mains is cleaner than gas, factoring in transmission efficiency and seasonal production/load.