Which truck / camp rig is taller (to the top of the camper including roof top equipment) and hauling the same camper: 1. F450 Cab and Chassis with a flat bed, or 2. F450 with pickup style box?
Assuming the bottom surface of the flat bed 6-8" above the top edge of the tires...that will put the top of the flatbed higher than the floor of the pickup bed which sits typically a few inches below the top of the wheels (the wheel wells allow for suspension articulation).
I would expect the camper to sit 10-12" higher on a flatbed...assuming all else is equal (ie: you don't change the tire size or do a lift kit on the pickup bed option)