The tow/haul button will do a lot more than you think. It is almost like moving the shifter into 3, but the little computer some how figures out that you have a load on the rear end. It will manager the shift points in the transmission based on the load you are towing, the amount of tork. I have tried it both ways.
https://www.chevyavalanchefanclub.com/cafcna/index.php?threads/tow-haul-button.8761/

