The GCWR's are the same auto to manual when you talk the same rear axle ratio. 19,000 for 3. 42's, 21,000 for 3. 73's, and 24,000 for 4. 10's. From there trailer rating is the GCWR minus the GVW. The auto is about 75lbs lighter (which seems weird) than the manual.
Even thou you can only get 3. 73's with a manual the final drive is actually higher on the manual than the auto with 4. 10's (which in my eyes means it should have the same or higher GCWR). .
GCWR is really only based on the ability to get a load moving. . because there is no physical difference in a truck with 3. 42's and 3. 73's. . assuming all other options are the same.
Manuals used to have a higher rating because they used to have more hp... now its the same for both.