I just went thru the same exercise.. 2012 F250, 10,000k GVRW. 3380 RAW on scales, 6100 RAWR. leaving 2720 of documented capacity for pin etc.
the GCVWR for both the 2012 F250 and F350 is 23500. so I could PULL a lot, just not 'carry' a lot. the F350 SRW highest RAWR is 7000 ,with a GVWR of 11,600. (note that the 1600lb increase in capacity doesn't all go to the rear axle)..
now, the truck TIRES were rated at 3850 each (80psi). for 7700lbs.
the 250 and 350 axles/brakes are identical. So technically the 10,000lb GVWR is a paper registration thing only (as noted some states charge commercial rates over 10,000lbs).
I wasn't willing to be overweight, even on paper. I couldn't afford the difference in a 250/350 srw trade. (best I found new was >6k difference)
but I found a same year dually for less than 1/2 that difference, with 1/2 the miles of my 250 (6500 vs 13000). and we had an 08 dually before the 250, and loved how it towed. but hated the fuel cost.
so now we have no weight worries. I know lots of folks that tow large with 250 shortbeds. I just wasn't willing to be one of those.
(and yes, the ride is rougher in the dually, but the rancho shocks and airbags have helped immensely).
Sam