The question is often asked, why under the floor?

   Although there is absolutely no difference in the efficiency of the two methods, there are advantages and disadvantages to each method.
--Installing the tubing on top of the floor with lightweight gypsum has the advantages of:
    Makes the tubing installation easier. 
    Helps to soundproof the floors.
    The thought of an increased thermal mass helps as a selling point.
    Can help level uneven floors.
The disadvantages are:
I have seen this stuff turn back to dust in high traffic areas.
      Increases the cost dramatically. 
Gypcrete has a history of complete failures   SEE GYPCRETE PROBLEMS
     Gypsum based products turn to mush if they get wet just like sheet rock.
     The added cost
     The disruption in the normal building process
     Makes zoning difficult
     Requires floor reengineering to support additional weight
     Has a influence on earthquake protection
     Requires expensive and confusing mixing valves and controls on boiler
     Complicates installation of floor coverings
     A leak can cause extensive damage to the sub-floor
     Does not install well in retrofits
     Has streaking effect on heat output
     The performance of the product rests totally on the installer, the manufacturer only guarantees the condition of the product at the time of shipping.
The advantages of installing the tubing under the floor are:
     More even heat output.
     Much less expensive.
     Does not require changes in building procedures.
     Tubing damage is easy to locate and repair.
     Does not require expensive or confusing mixing valves.
     The home owner can install the tubing himself with proper instruction.
     Installs easily in retrofits.
     Under the floor eliminates streaking of surface temperature. 
-- The disadvantages of installing the tubing under the floor are:
     Some can be noisy.
     Tubing installation can be slower.

  I do not recommend Warmboard, it is very expensive, causes streaking, the foil adds nothing and if the tubing is ever damaged it will delaminate the plywood. When installing pex tubing remember it will be there one hundred years from now, you need to consider what effects it will have on later remodels and changes to life styles.   

  Although it seems to make since, a layer of aluminum foil sandwiched between subfloor and floor does not spread the heat nor does it add mass. Putting gypcrete on top of the floor adds very little mass because the tubing is so close to the surface. The fact is that mass has very little to effecting a radiant system until the power goes off and certainly has no effect whatsoever on the efficiency of a radiant system.