I've driven a Ford V10 with 3.73 gears and 4.30 gears and all the way through the gears the 4.30 wins hands down, I have friends with 6.7 Fords with 3.54 and 3.73 gears again the lower gears win. One of my Ford trucks with a 460 I changed from 3.73 to 4.10 night and day difference pulling the same load.
The 6 speed makes a dig difference because the second OD keeps the rpm down when cruising down the road in 6th pulling because the final gear ratio puts more available power to the ground.
No what is said the final mechanical advantage (rear gears) makes the difference, just go to any truck specs and see what happens to the towing capacity increases with lower gears.
Denny