The styrofoams that are recommended for underslab use show virtually no short or long-term compaction. They're very rigid and are almost structural in their own right. The way they're installed also greatly increases their ability to bear weight without compacting.
Think of it this way...
The slab and the panels are dimensionally very close to the same size -- that means that the entire surface of the styrofoam is bearing the weight of the slab, giving an extremely low pounds per square inch value on the styrofoam.
It's like when you go out on thin ice... if you're standing, all of your weight is concentrated on your feet, and you'll crack the ice surface. If, however, you lay down, the ice can support you because your entire weight is being supported by a much greater area of ice.
Granted, the installation of panels is much fussier than the tarps because the subsurface has to be very flat and very well compacted. With the tarp, you don't have to spend nearly as much time leveling the surface -- it still has to be highly compacted, though. If it moves, the slab is going to crack.
Don't get me wrong, I'm not advocating one against the other. I can certainly see advantages to the tarp, if it works as advertised.
Hum... In reading through the Insultarp information it's being a bit disingenuous... It gives the impression that there's no under-slab foamboard on the market that can mitigate radiant heat loss. That's a lot of "hot air" so to speak. Slab-Shield is but one of the faced under slab products on the market.
Oh SNAP!
Check out the letter from the Federal Trade Commission on this website:
http://www.thebarrierinsulation.com/7128.html?*session*id*key*=*session*id*val*
"...it may be misleading for industry members to suggest that such foil products will reflect radiant heat
when installed under concrete.Interesting. And the underlining is in the letter...