Not much info available. The order guide for a 2005 and 2006 F-550 said only that diesel engine and 4.88 limited-slip axle was required, and that the pkg included an "upgraded" rear axle. The axle is a Dana/Spicer 110, but somehow the one with the high capacity towing pkg is different than the standard Dana S-110 limited slip 4.88 that is optional in the F-550 without the high capacity towing pkg.
The 2006 Ford Truck Source Book says the F-550 has a Dana S-110 rear axle rated 13,600 pounds, and a footnote says that with the high capacity towing pkg the axle is a Dana S-110 "with a unique 4.88 axle ratio gear set". That doesn't mean that the 4.88 ratio is unique, because all 2005 and 2006 F-550s with diesel engine had a 4.88 ratio. Nothing else was optional.
I know zippo about differentials, but apparently the "unique" S-110 limited slip diff 4.88 with the high capacity towing pkg is somehow beefed up compared to the normal S-110 limited slip 4.88.
One guy that can probably explain the subtleties of the difference is member username Robyn. Robyn is his wife's name, but he's a big ugly dude so don't let the username confuse you.