Ford Markets a 10000 GVWR F350 SRW and the same identical F350 SRW in a 11200 GVWR both with the same 17" tire and wheel package in say a crew cab 4x4 6.7 diesel 172.4" wheelbase truck. The biggest difference is the SRW has a 6290 RAWR vs a 6200 RAWR on the F250.
And looking at Fords fleet specs shows the 10k GVWR F250 has a bit more payload than the same configured 10k GVWR F350 SRW truck.
Now the OP can get a 11500 GVWR F350 SRW with a 7000 RAWR and a 37xx lb payload in the same 172.4" wheelbase crew cab 4x4 6.7 diesel truck. However a 16500 lb RV trailer can have too much pin weight (3200-3500 lbs) even for this truck.
If the OP chooses a F250 he will have to upgrade the trucks rear spring pack big time and go with the higher rated 18" or 20" tires and wheels for a 16500 lb trailer that may have a 3300-3500 lb pin weight.