Any determination of "should" is going to be highly effected by how long the owners will own the house, fuel used and the ROI available from other things. Even the expected floor temp (the radiant case), the soil type and floor covering changes the numbers.

Jonr,

You are right about various factors affecting the answers.  In this particular case, the footers for this home will be built upon bedrock.  The two foot of space between the bedrock and the bottom of the slab will be filled with compacted, clean gravel and some expanded polystyrene (EPS).  The clean gravel will be used primarily to contain waste lines and to keep water from rising by capillary action.  My guess at this time is that the basement slab will be about 5 to 6 feef below grade.  At this point in time we are not concerned with Return On Investment.  With all of this in mind, what should the R-values be?

Without details, I'll guess 2" of EPS for both cases. The same value since in the unheated case, comfort becomes an issue (depending somewhat on floor covering).

IRC 2012 calls out R0 for non-radiant slabs in zone-3. (Huntsville is on the cool edge of zone 3)

BSC thinks R5 still makes economic sense for non-radiant. (See table 2, p.10)

Any time you're making the slab into a heat-emitter, adding another R5 (in warmer areas, with short heating seasons and warmer subsoils) to R10 (longer heating season, colder subsoil) makes sense.

For a PassiveHouse would put you at more like R20-25 under the slab in Huntsville.

So, 1.5-2" of EPS would probably do it for non-radiant, call , 2.5-3" if radiant.   EPS is preferable to XPS in this application on long-term R-value and the 200x greater global warming potential of the blowing agents used.  Type-II EPS is fine under a residential slab, but if some inspector thinks you really need the 25psi compression spec that most XPS has you'll have to bump up to  2lbn density Type-IX EPS, which is usually no more expensive per unit-R than XPS, if somewhat more expensive than Type-II.

Alton,
I have used 2" EPS in non-radiant slabs, with good success. Make sure to insulate the edges of the slab. ICF's do a good job of that. But if basement wall are concrete, you want to provide a thermal break between walls and slab.

Thanks to everyone for their comments.