“What are the pros & cons of dual-fuel heat pumps vs. modern, inverter-based heat pumps?”

Trane makes a unit with a heat pump and a back up gas furnace that they call a “dual-fuel unit”. It does not really use two fuels, it uses electricity to run the heat pump and uses natural gas to run a furnace as a back up for when the heat pump can’t keep the house at the temperature set on the thermostat. This type of unit makes sense in new construction. In existing houses, they already have the furnace so adding the heat pump gives you the same result. In NE you really need this set up. In NC you could probably get away with a cold-climate heat pump and no furnace. If you get one or two days when it is too cold for the cold-climate heat pump you can always use an electric-resistance fan heater to top it up.