When you click on links to various merchants on this site and make a purchase, this can result in this site earning a commission. Affiliate programs and affiliations include, but are not limited to, the eBay Partner Network.
Chances are if you're pulling a fifth wheel or gooseneck with an F250 CC 11K is too much. About 20-25% of that weight is going to be on the truck, which would be a minimum of 2200 lbs. Go weigh your truck and subtract that from the 8800 GVWR and you'll be surprised how little payload you have left.
To give you some idea of the weight of an F350 SRW CC 4x4 w/V10, mine weighed 7500 lbs. with a full tank of gas and me & wife in the truck. As the F250 & F350 SRW are basically the same, this would only leave 1300 lbs for pin-weight for goose-neck on an F250. The SRW F350 has 2400 lbs available payload capacity. The F350 dually would have even more!
As for your question, regardless of tow method, the GVWR and GCWR are set by the manufacturer. Goose-necks & fifth-wheels are the same. Tag-along (bumper pull) weight ratings are generally lower than goose/fifth ratings. However, a "bumper-pull" trailer only puts 10-15% of the weight on the truck. So, with an F250 CC, it's possible to tow more (without exceeding GVWR) with a bumper-pull trailer than with a goose-neck/fifth-wheel. However, I think tag-along trailers are much less stable than goose/fivers.