First, don't get confused by power spent vs power gained. Heat pumps move energy around, so it's possible for a 5000W heat pump to move 15,000W of useful heat.
Second, don't get confused by
- power (rate of flow right now, e.g. 5000 watts or 20,000 BTU**/hour**; 1 watt = 3.412 BTU/hr) versus
- accumulated energy (flow x time, e.g. 5 kilowatt-hours or 20,000 BTU, 1 kwh=3412 BTU).
Worse, "BTU" in many contexts actually means "BTU/hr", e.g. In the spec for furnaces.
When you're near your desired temperature, your house loses energy to the outside at a certain rate (i.e. power) depending on outside temperature.
Suppose you lose 3000 watts through leaks through your insulation. OK, if your heating is 4000 watts, you can see where you're only gaining 1000W/hr and this is gonna be a slow run. Increase heating to 5000 watts and your net heating doubles and the time cuts in half. Or improve insulation 33%, same effect.
The upshot is that if you want speed, you wants lots of immediate power: lots of watts of heat generated, or BTU/hr.
Jimmy Fix-it makes the point that you don't want speed. I don't see why not. He's talking about the additional infrastructure costs of installing more heating capacity. Okay. But if you like to change temperatures, a system that can do this quickly saves money over doing it slowly. If you are using a predicting smart 'stat, better to have it kick 30 minutes in advance than 3 hours, because that's 2.5 hours of thermal loss you won't have.
If you're all-electric, you are partly limited by a) your service's ability to supply power, b) your wires' ability to carry it, and c) your ability to pay a fat heating bill.
With that in mind, heat pumps are much more efficient at turning watts you pay for into watts that warm your house. In the above scenario you replace your 5000W heater with a 5000W (consumed) heat pump. It will bring into the house 10,000-15,000W (pumped). Now instead of gaining 2000W, you are gaining 7000-12,000W. Which means your house warms 3-6 times faster!
Heat pumps do have an Achilles' heel. They don't work if the outside air source is too cold. Did I say air? Why are we talking about air? If you dig a hole deep enough, the ground never freezes. At very diggable depths, things are quite temperate, e.g. 55 degrees all year. Well water is like that. This is an ideal temperature for heat pumps to work both for heating and cooling, and you gain even more efficiency. So a perfect situation is the ground-sourced heat pump, where it's operating from groundwater, a coolant loop dug deep enough into the earth, etc.
However if you can't ground-source your heat pumps, then you need to contend with a nightmare scenario of the outside air being too cold for the heat pump to work at all. This is less of a problem in better, newer units. In that case, the system "fails over" to resistance heating, exactly what you have now, and the electricity cost can hurt!
There is one way around that "nightmare scenario" but it's very trailer-park. Build an insulated structure over your outside heat pump unit, so it's "inside a building". Heat the interior of that building with fuel of some kind. It will need to be a BIG heater, since it's heating your whole house via the heat pump. Now the outside unit will be in good temperatures for it to work, but you'll have a fuel bill. "But that sounds terribly inefficient" sure, it's a hack to use a few days a year. On the other hand, institutional sites do pretty much this, with heat pumps all over the institution sourcing to service water which runs all over the complex. In winter, they pre-heat the service water to about 70F. So it's not that extreme or bizarre.
If you don't want ugly air ducts all over your house, they make "mini-split" units that run thin, concealable freon pipes around your house instead. This also lets you zone your heating and A/C. All heat pumps come with A/C.