Insulating below slab-on-grade floors

That is a common question, and a hot topic that often brings dissagreement, but we like that though!  So much so that we have a page highlighting the pros and cons, check it out - 

Slab on Grade or Foundation and Basement; Which is Best?

But to address your questions specifically, I've included your questions in the response to make it easier for both of us - 

1. Cost - I know a slab is cheaper but having a basement that we can finish allows for a smaller footprint with less walls and roof material.  Is there a big difference in cost? 

We have typically found above-grade walls to be a more affordable building option, but no, it is not a huge difference. A basement will result in a much higher excavation cost to begin with, but also, concrete is a more expensive structural material compared to wood, so an above grade wall assembly can usually achieve a higher performance level for a lower cost since you can use wood as the structure. Yes, you will have a greater amount of above grade wall to build, but as mentioned, that can cost less than the same amount of below grade wall.

On the other hand, there are ICF advocates (insulated concrete forms) that would argue in favour of basements, including bottom to top ICF walls; those builders would argue there isn’t a great difference in cost.

Personally, I wouldn’t base the decision as much on cost as a few other issues, namely: durability, quality of life, and ecological impact. Cement manufacturing emits a significant amount of greenhouse gases, and sand that is suitable for concrete production is becoming an increasingly scarce global resource, where wood is  renewable. that's why we as an organization like to promote the more sustainable options, and limiting the use of concrete is a large part of that, ergo we like slabs.

As for durability – basements walls cannot dry to the exterior, so more caution must be taken in designing and building walls below grade. Also, basements flood, that’s just a part of life. We can take steps to mitigate that with drainage and sump pumps with battery backup systems in case of power failure during storms, but it is impossible to predict levels of precipitation long into the future except to say that it doesn’t look good. If your house is above grade and not in a flood plain, you will never have to worry about it flooding. 

2. Access for mechanical - I can't get my head around having to embed drains, plumbing, electrical, etc in concrete as opposed to putting it under floor.  Not to mention running ducting for ERV.   Is this a valid concern?   What if there is a leak in the drains, how would you ever know?

More than being a valid concern is the part about wrapping your head around it, so that's all relative. I have no problem with embedding the infrastructure in the concrete  but I would have a hard time wrapping my head around the idea of digging a hole in the ground to live in it when I could be living above grade. It's more a matter of what you're used to, if you go to California for example, you'd have a hard time finding a basement because they build all their houses on slabs and don't give it a second thought. And... if a drain DID have a leak and a the occasional drop made it to the ground below, no you probably would not know, nor would you probably care.  

Where concern is valid is - you cannot change plumbing in the future so you need to be sure you are happy with the house layout to begin with. In order for a drain to leak you’d have to screw it up in the first place. So hire a licensed plumber and don't worry. As for the water feeds and electrical lines, they should be put into conduits (a sleeve), so if there ever was an issue you can pull them out and replace them. HRV ducting should not be run in the slab, that should be run through walls and ceilings only. 

3. What about a hybrid - we don't need a full basement, what are the implications of having half of the footprint as a slab, and half basement?

A hybrid can be done no problem, but it would add cost and building complication, so if it were me I wouldn't do it unless there was a very good reason due to the building terrain a house was to sit on. A hybrid would  still leave you with embedding stuff in concrete as well as the durability concerns of a basement, so that sounds to me like it will ensure you are concerned out about it whichever one you choose :) 

We are currently building a new demo house, on a slab, here is a video of the install if you want to have a peek. It is entirely above grade, and as I write, the house on top is being built, which will be insulated with cellulose (recycled news print).
Here are some other pages on slabs for your interest. Don’t hesitate to write back with more concerns, we love slabs and are happy to keep the discussion going. 

• Best practices for insulating basements
• Choosing between a slab and a basement
   

You are right that heat escaping from the exterior edge or footing of a slab will help prevent frost heave, and that the more you insulate, the less heat will escape, increasing the risk of damage. And the way to mitigate that risk is to install a perimeter skirt insulation (where and when it is needed). This is exactly how we would build a slab, so we rely on insulation to protect the building from frost damage rather than relying on continued heat loss.  There are a couple of pages that I think will help you a lot, first this one - 

How Much Insulation Does a Basement Floor Need?

And here is a page about slab on grade premade form kits, this is by a company called Legalett that provides slab on grade kits that mean you can stop scratching a hole in your head figuring insulation levels, they do it all for you. We just built one ourselves, here is a slab on grade DIY installation video so you can see how quick and easy it goes together. 

Further to that, there are a few variables at play that need to be considered when designing the slab to ensure durability: The AFI (air freeze index), how much insulation encases the slab, the soil conditions, and whether or not the slab will be heated. The best way to ensure that a FPSF (Frost-protected shallow foundation or slab-on-grade) doesn’t heave would be to have it modelled for your specific climate by an engineer, ideally a geotechnical engineer. 

In general terms and as a point of reference only - our experience with slabs in Canada is that R20 like you describe is not extreme, nor does it always require a skirt. But without the benefit of a proper climate analysis we cannot make any design recommends for you, and without such information I would for sure take the safe route and install a skirt.

As for your choice of insulation, why XPS (extruded polystyrene)?  EPS (expanded polystyrene) is a lot less harmful in terms of green house gas emissions during manufacturing, and is about half the price. XPS has a higher R value per inch (R5), but space wouldn’t be an issue since you are building on grade so I’d suggest you save some money and emissions and use EPS (R4 per inch). You would get a much higher R value per dollar. Here you can see our page about how to choose the best rigid insulation board.