The advantages of a built in
furnace include a thermostat that will hold a temperature and keep pipes from freezing when you are away. They tend to consume more fuel.
The advantages of many portable heaters, electric or
propane include reasonably holding a temperature for an extended period, including while you step out. It is hard to boondock with most electrics. You may not feel safe leaving some
propane heaters unattended, but they vary.
Among the advantages of small wood fired stoves include vented chimneys, and their charming, dare I say romantic flames. Some provide too much heat for a small
fiberglass rv. They also require front and side clearances. Seems to me the biggest drawback is that due to their small fireboxes, they require nearly constant tending, are harder to regulate, and don't keep things from freezing when you leave. They do work when
boondocking, assuming you have small pieces of dry wood. Obtaining and prepping wood? No thanks.
I suppose the answer for many lies in a combination. Tiny electrics when not
boondocking, and a funace perhaps, or portable propane heater when
boondocking. I just bought an Olympic Wave 3000, and have a tiny ceramic cube.