You can use the 15psi foam under the slab, but if you are going to put some significant point loads on the slab, 25psi is a better choice...the loading could be as simple as a floor jack under an f250, for example.
The insulation is advantageous for a few reasons.
1) The perm rating on EXTRUDED polystyrene makes it a very effective vapor retarder by itself (do not use the white beadboard...it is EXPANDED polystyrene and an absolute no-no in this application).
2) It will not absorb moisture. This type of material is used for floatation billets for decades without any appreciable gain in moisture. This will aid in the hydration of the concrete and give you a higher quality slab...much in the same manner as visqueen would do for you.
3) The insulating value of the material will remain constant. It has an r-value of 5 per inch, and this is the aged r-value. In this application, there is no other insulation board which will retain it's r-value over time to this degree...again, water absorption has a lot to do with this.
4) Here's where the insulated slab really gives you performance...
By insulating the slab in a VERY effective way, and eliminating the thermal bridging to the exterior and substrate, it now takes on the ambient temperature. This does a couple things for you. It now is not a colder temperature than the surrounding air in the spring, so it will not form condensate. If you have ever had a problem with a wet floor, this is one of the two causes...it's either moisture drive through the slab from the ground, or condensate from reaching the dewpoint somewhere within the slab. You have now eliminated both of the conditions that make this moisture appear.
Last, but by no means least, you are now using the mass of the concrete to your advantage. Yes, on a hot day, an uninsulated slab will be cooler, but that really does not add to any comfort for the inhabitants for the most part. If you are heating or cooling the garage, the mass of concrete will take on room temperature. In cold outside conditions, the concrete will take on heat energy, and when you have a door open, or bring in a cold car or equipment, that warm concrete slab will help reduce the spike load on the heater. It gives off btu's to the surroundings. Basically it's a giant thermal flywheel. The same thing, but in reverse happens if you run an air conditioner...hot car brought into a cooled garage with cooled slab will be able to absorb a lot of BTU's, and let the air conditioner deal with those btu's over a longer period of time, and act more efficiently.
The biggest benefit you will see from a HVAC performance area is in the winter when you are heating. In the summer, the insulation in the slab does not help you as much in that way, but the condensate issue is the key here during the spring months.
This enhanced mass performance is something that we can calculate quite easily, and it is a set of equations from ASHRAE, from which mechanical engineers base their load requirements for sizing the mechanical systems in all facility types.
. I do A/C work and since I am in the south I am installing a central heat and air unit for those extremely hot days. My question is my contractor is saying we don't need the plastic sheeting moisture barrier like they do in homes , I am thinking you do because of the humidity here and the fact that I am painting the floor along with airconditioning it. What do you fellows think about it? Thank you in advance. 
