It all makess a difference, but the diff ratio does the most or has the most impact...all other things equal
Just look at any OEM MTWR (tow rating) or GCWR (gross combined weight rating) chart
Note that these are all 'stock' vehicles and 'stock' engines. Within anyone of them...there are two or more MTWR or GCWR and the difference is in diff gear ratios
GM....as the OP has a GM/GMC pickup...and as always...note the fine print qualifying those MTWR's that is on ALL OEM specifications. Also note that he went to 4.10's, which is off the charts so to speak...
GM TRAILERING AND TOWING CHARTS
For the Ford folks
Ford F150 2016 PickupFor the RAM folks and chose the 3500 to show that this is NOT just a half ton thing, but any sized rated truck...even cars, but there are no charts for towing that I could find
RAM 2017 3500 towing