Just do the math, all you need to know is furnace efficiency and COP of the heat pump along with the efficiency of your local power plant. I did that in my post

Just do the math, all you need to know is furnace efficiency and COP of the heat pump along with the efficiency of your local power plant. I did that in my post, its not super complicated. Gas is burned creating a certain amount of heat, in a furnace some is lost to exhaust the rest goes into your house. That is the furnace efficiency. When gas is burned at a power plant the same number of BTU is released, but it is used instead in a heat engine to create mechanical power which is then turned into electrical power, the rest is lost to exhaust, this is the power plant efficiency. Heat pumps are over 100% efficient because they capture heat from the environment around your house which is warmed by the sun. So even though more energy is lost in creating electricity than burning directly in your house, this is more than made up for by using the ambient heat around your house, it is essentially solar assisted (in the case of air source).