There are set towing capacities, the DRW trucks are set up to allow heavier loads, and you should check your insurance and state laws before pushing those ratings. (I don't want to make this a legal debate).
There are differences in the rear axle weights between the two trucks. (the SRW's are Sterling 10.5" vs. the DRW's Dana 80s (F350) or Dana110 (F450) with 9K of RAWR or more (after '05). Also the transmission coolers are bigger on the DRW trucks (again after '05). So there will be differences on what kind of pin weight you can carry with similar overall wieghts (again factors into the stability).
Where you start seeing the true benefit of the DRW truck, is when you feel the stability of the load, and should you blow a rear tire out, you have more control until you can pull over. Personally, I wouldn't have a dedicated towing vehicle that wasn't a DRW, and feel that once you cross into that 10-12K load routinely, you are sellling yourself short with a SRW truck.