Doing the same thing in a 58 year old basement with dricore (local supplier called SubFlor here in Quebec, Canada). Their website has instructions on framing either outside or on top of the dricore.
http://www.subflor.com/ADVANCE/install.asp
If you choose the option to put the framing directly on the concrete, make sure you put a foam sill gasket underneath the wood.
After a sewer backup/flood in May, I had to redo my basement bathroom. I will be using a mix of BluWood directly on the concrete pad (with foam sill gasket) and on the dricore (SubFlor) with screws that do not breach the OSB top (framing depth = 1.5inch plus .5inch into SubFlor).
I have had the SubFlor installed for 3 months (I work on a limited time budget - my wife is p/oed that I really take my time on projects

) but the upside is that I can confirm that it has completely eliminated the efflorescence whcih was there previously with tar paper under (rotted out) 2X3 wood framed subfloor - plus I gained more room height (SubFlor = 7/8 inch, previous 2x3 sub floor + 1/2inch plywood = 3inch, net gain = over 2 inches).
Whichever, don't forget the 1/4inch expansion gap around the dricore and the caveat about wrapping the vapour barrier.
Pictures attached (first = new dricore, second and third = rotted plywood in old bathroom, fourth shows new plumbing rough in) - framing will (hopefully) be done this weekend - will post pics later.