Nope, the 5.3 can tow up to 11,000 pounds, the 3.0 diesel is at least 13,000 pounds. 6.2 gas is 100 or 200 pounds more than the 3.0 diesel, all according to the configuration of the truck.
GCWR for the 6.2 gas is 19,100 pounds.
GCWR for the 3.0 diesel is 19,000 pounds.
My findings based on...