Boatycall's analysis of the 2015/16 F450 was spot on except for one minor detail that gets missed quite often. The rear axle is actually a Dana S130 not the 110, and it's rated for 16k pounds from the manufacturer not 14k.
A couple other items of note, although there are fewer leaves in the F450 spring pack, they are considerably thicker then the F350 DRW with a stiffer spring rate. The front frame clip is the boxed version borrowed from the F450/550 chassis cab, as are the front suspension components....take a peek under there, they are huge!
About the only advantage the F350 max tow would have is a softer unloaded ride with the 17" E rated tires and softer rear springs.
Stepping up to the F450/550 chassis cabs gets you monster payload capacity, but at a pretty steep penalty for some buyers. You have the additional expense of a flatbed, and you end up with a de-tuned motor that takes a big hit in power. We're talking 440hp vs 300 for the cab and chassis, and 860ft/lbs vs 660 of torque.
Those aren't just de-tuned with programming either, they have completely different turbochargers on them.
For most folks hauling a heavy camper, the F450 pickup is the best overall bang for your buck.