tvromero,
After having done research for another tow vehicle, I would recommend looking at the towing guides on Trailer Life web site. The guides will give you the towing capacity. Example: the 2016 Silverado 3500 SRW 4x4 Double Cab will tow a 17,000# 5th wheel. It also gives TT capacities.
As the percentage of pin weight goes up the amount you can tow goes down.
Payload data don't really tell you how much trailer you can tow. The diesel will get better mileage than the gasser. Even with that, I went with a 2005 Silverado 2500 HD with 8.1L (496ci) and Allison Transmission. It is rated for a 12,000# travel trailer or 14,000# 5ver.
Take your time and get the one you like best. Check the towing capacity with the GVWR (loaded weight) of the trailer.