The Tow Haul function is to save wear and tear on the transmission. GM recommends using it when the vehicle and trailer load exceed 75% of the GCWR of the truck. I use it even with a much lighter load when going up or down steep grades, where as mentioned, it helps the grade control system in the truck to keep your speed under control without having to do much in the way of braking.
The GM grade control system only works with the transmission in Range selection or manual mode. One situation where Range select mode is useful is if there is low traction as you can go into Range select and put the transmission into 2nd gear and this activates what GM calls "low traction mode".
I have never experienced anything workings nearly as well as the GM grade control using the transmission in auto and the Tow Haul mode engaged. It is a very impressive bit of engineering and the result of careful coordination between the Duramax, GM, and Allison engineers. About 10% of the time when using Tow Haul down a very long and step grade if I see the speed climbing I will engage the Exhaust Brake with the switch on the dash. With the newer trucks you can engage and disengage the exhaust brake at any time.