On my traverse (2010).
I Notice the difference mostly in 1st/2nd gear- where it holds the rpms longer and higher.
I have not towed-- so cant say what it does under load.
Why does your post show that it's ignored? I had to click on the box under your profile info to see this. I don't have anyone ignored. I don't dislike anyone on here, seriously

Anyways, I did notice that it did seem to hold gears a little longer, not much and not really that noticable but a little.
Though I don't have the tow option, I believe that others here have mentioned that the transmission stays in 5th gear while cruising for better throttle response.
I did notice that it didn't seem to shift into 6th where is was before. My speeds where only around 45 tops when I was testing it though.
Is the Two-Haul-Mode supposed to down shift the transmission faster when braking to help slow down faster, taking some of the load off the brakes? That is how it works in my truck. In my truck there is a noticable difference in how high the RPM's go before it up shifts. This system in my Enclave doesn't really seem to be doing much of anything when it's on, seems like there is really no reason to pay the extra mony for the option if this is all it does.