IMHO the GVWR of the F450 does not increase in proportion to the strength of its components, which is why the payload capacity is actually LESS than the F350 DRW. Not sure why Ford plays this numbers game, except maybe to help keep the cost of licensing and insuring the truck down somewhat, to make it more attractive to buyers.
Compare the axle ratings for the two trucks, and the empty/curb weight of the two trucks. I would expect FAWR+RAWR-CURB for the F450 to be at least 1000lbs more than the F350 DRW. Maybe I'm totally off my rocker here but that is what I would expect.
Probably either would do the job for you, but I feel that the F450 with its heavier components would do the job longer.