Walking a dealer makes me think the F250 has D rated tires and the F350 has E rated. D, as a general rule carry less weight. The payload and axle rating are set due to a limitation. In this case, I think the limitation is the tires.
Tire places are not supposed to put lighter tires on trucks for liability reasons...heavier yes, lighter no.
I was at Discount Tire and a guy was throwing a fit because they wouldn't put a P-rated Tire on his F250. He said he wanted a smoother ride and doesn't haul anything. If you put P rated tires on your F250, the tires may be rated at 2250lbs each. Making your payload 346 pounds because the tires are now the weakness. An over simplification but gets the point across.
If you put 19.5s on it rated at 3900lbs per Tire, then your next weakness, probably spring rate will set the limits.

 

The axle on my F450 from Dana is rated at 13,600 pounds. The tires (4) are 3750lbs each, so tires are good for 15k. Those sissies at Ford put a spring pack rated at only 10,300. So, Ford sets the rear axle limit a 9,990lbs even though Dana and the tires are rated higher. Put airbags on it, the next weakness is the axle at 13,600lbs. The bags will not legally change the axle rating, just makes it brake and steer better and oncoming traffic won't flash their lights at you.

 

I'm convinced the specific ratings you cite are arbitrary/because Ford is lazy. The 250 rear GAWR doesn't show a change with the high cap trailer package which has the same axle as the 350 SRW. If this is a tire limitation, then why add the upgraded axle and spring pack??

Ultimately, IMO if you are buying a new truck and you intend to have a significant payload in the truck often, just spring for the 350, for the ratings. I regret that for moving my camper but I don't move it far or often, so I just deal with it.

 

I'm curious. A F250 with HCTP, does it have load range E rated tires? Is it just a gearing change from. 3.31s to 3.55s? Anyone else know????

 

I have a 21 with it, I don't remember what tires were on it, but it has the M275 and the same leaf pack that the 350 SRW has, and GVWR is 10800 vs 10k. Mine had 60-65psi in the tires I think, but tires were changed after I think 3-4 weeks.

I think the 24s are using an 11.6 sterling that the 350 SRW has, and the same leaf pack.

I think some years the 3.55E Gears required the High Cap package on the 250 but I haven't paid close attention, looking now the 24 Build & Price tool does require it. Makes sense from Ford's perspective, don't need the 3.55E gear setup for the 10.8 axle, saving money, and it forces you to jump to the High Cap Axle package which is $1130.