The heat pump will work for most situations, and when you are connected to shore power.
1) It is a bit noisier than the furnace.
2) It doesn't really work well at near freezing temperatures outside, but with the heated mattresses in most units it will be enough to keep you warm.
3) it will save you from using the gas at the furnace uses.
4) it will minimize the effects of interior condensation as the LP furnace can add to water vapor in the small space of an A frame.
I usually just use the heating function of the heat pump, but either should work well for you.
Audi Q5 + 2015 A-122S = happy camper!
2015 A122S "The next campsite tour of this type of intriguing camper will begin in approximately 15 minutes. We ask that you refrain from any flash photography as it tends to wake the native inhabitants..."
Camped 6 times in 2014, 5 times so for in 2015