The axle tube wall thickness heavier on the F350
Sorry I have still not found parts numbers, but found this,
from Wikipedia:
F-250, F-350 & F-450 pickups
A feature unique to the 2011 Super Duty is the addition of a locking differential. It is only available for the F-250 and SRW F-350 4x4 models with a rear Sterling 10.5 axle. It is a 390.00 USD option [14] There are mechanical differences between the F-250 and SRW F-350, despite looking identical. The diesel F-250 relies on vacuum-boost brakes, while the F-350 relies on Hydro-boost. Both gas versions of the F-250 and SRW F-350 use vacuum-boost. F-250 is a class 2 truck. While the F-350 SRW, F-350 DRW, & F-450 pickup are class 3. F-350 SRW rear axle has thicker axle tubes. The F-250 and F-350 (SRW & DRW) have 13.66 inch front brakes and 13.39 inch rear brakes. The F-450 pickup has 14.53 inch front brakes and 15.35 inch rear brakes. The F-450 has a wider track than the F-350. The F-450 remains available in class 4 as well.
