I would agree that under the floor would be the best way, here is what I see as the advantages and disadvantages of each.
Insulating over existing flooring: This would be by far the easiest way to go. If you use a good quality rigid insulation designed for under concrete slabs, you could use a 2" thickness with a 5/8" to 3/4" Plywood (tongue and groove preferred to ensure an even floor) over the foam. The plywood will spread the load out evenly over the existing floor and you can screw the new plywood down through the foam into the existing wood floor with long deck screws. I would install wood sleepers at the perimeter of the box to fasten the edges down to, the foam itself will support the load elsewhere. (If you have a garage area and plan to load a vehicle I would place some wood sleepers under the path of the tires, and anywhere you install a tie down) Then build out your walls on top of the new floor. With the insulation continuous over the whole floor you will not have any cold spots, or thermal transfer through the steel framing under the floor. There will be no worries of any trapped moisture or water from the exterior assuming the floor was weather proof to start with. the insulation can be grooved out on top in places you want to run wires or plumbing.
Insulation under the floor: Kenn is right that this way will take up less box space and keep your floor as low as possible, but it is not without its issues. Unless the box is off of the frame it will be difficult at best to get rigid insulation installed in many places. Steel framing members will be penetrating the insulation layer and transferring cold up to the bottom of the floor. The biggest issue would be keeping water and moisture from getting trapped in the insulation, this can cause rot and mold on wood surfaces and rust on the metal. A good quality closed cell rigid foam will not absorb water, but you will need to a good job sealing around the edges. Having expanding spray foam installed would be the best as it gets into every crack and crevice and does not leave edges to seal. However not a cheap way to go. While I have seen unprotected foam insulation under some conversions, possible damage to the foam from constant exposure to the elements, and debris coming off the road surface bothers me to much to leave it exposed. It may be possible to install a sheet metal underclosure, but again that would have to be sealed to keep out the water. Perhaps a spray on under coating designed for cars would create a water proof protective shell. I have not looked into if it would be compatible with foam insulation.
With all that said, If I were building from scratch or had the box off the truck, I would probably go with insulation under the floor, otherwise on a build out of an existing box I would more than likely go with on top of the existing floor.
Anyway my $0.02
Dave
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