Well, let's start off simple: you need a certain number of BTUs to heat your home on the coldest day of the year. There are a lot of calculations to figure that out, but that's why there are geothermal guys. The way to compare furnace systems (wood burning stove, gas furnace, etc.) is to ask how much energy and what type of energy it'll take you to get the BTUs you need, as well as how efficiently each unit converts energy into BTUs.
Geothermal is a way of substituting the energy from the sun into part of the energy you need to make BTUs. It does this by using the warmth of the ground to heat water (or whatever it is inside the pipes).
That's the simple version. The water that comes out of the ground isn't a whole lotta hot (somewhere in the 40s) so if you used it just as it came, you'd have a pretty cold house. Not as cold as the outside, but still really cold. So, they run the water in the 40s through a series of compressors that release heat by playing with pressure and the boiling point of the fluid inside the pipes (like a refrigerator does, one side gets hot and the other side gets cold). At that point, you can either blow a fan across the hot pipes (forced air heat) or transfer the energy to another liquid and pump that liquid through baseboard heat units (probably what I'll have in the basement), in-floor heat pipes (that's what we're doing upstairs), radiators, etc.
To compare:
The most efficient gas furnace will run you somewhere in the neighborhood of 90% efficient. For each unit of energy you add to the heat system, you get 0.9 units of energy out as heat. That's really good! I'd estimate my old furnace was about 15% efficient and that stank.
On the other hand, because the sun is supplying so much of the energy to the geothermal system, they wind up being somewhere between 300-400% efficient. For each unit of energy in, you get 3-4 units of energy out as heat. That's huge!
Now, the energy that we supply the geothermal unit is electricity and that kind of sucks, but for that kind of efficiency it's worth the extra energy cost per unit (especially when we'll be using so much less energy). And we're exploring the option of putting some solar panels on the roof as well.
Does that make sense?
I was just curious about those nudi's as one of the biggest complaints I read about is Aiptasia. 
