One of the big differences is that the 2013 F450 pickup was only available in 4wd with a diesel and you seem to imply that you wanted a gas burner.
Assuming that you are OK with the diesel and 4wd the big difference is the wide front end and rear axles. The wide front gives a shorter turn radius and the bigger rear axle gives more towing ability. However, while the GCWR of the 450 is higher than that of the 350 for more towing the GVWR is about the same. Since the 450 is a heavier truck it is actually rated to carry less. If you are looking at a chassis/frame with a custom bed F450 everything changes. Its GVWR is much higher and it rides like a truck.
Here is some good info for you to look at:
https://www.ford.com/services/assets/Brochure?make=Ford&model=SuperDuty&year=2013&postalCode=11738
http://www.trucktrend.com/cool-trucks/1308-2013-ford-f-450-platinum-road-test/
It is ironic that there are some many comments here in favor of the wide front on the F450. Ford offered that front end on the F350 for a while but did not have enough takers so they dropped that combination.