I hauled a Uhaul 6x12 loaded with furniture for about 300 miles of mostly interstate on Sunday. The base weight of the trailer is just under 2K and I would guess maybe 1K-1.5K of furniture in it. Any reason I should have had it in tow/haul mode? The engine only seemed to possibly be "lugging" in a short stretch of 45mph near the start, before the interstate. On the interstate, everything was good and it stayed in 8th gear for the majority of the trip.
I recently completed a 3,300 mile road trip, and probably 1,400 of that was towing a loaded twin-axle (6 x 12) U-Haul trailer. I noticed very little difference with Tow/Haul engaged or disengaged at 70-80 mph (3.92 gears). I was in 8th on flat stretches, 7th quite a bit with headwinds or gentle grades, and 6th on steeper hills. The truck would even go into MDS on gentle downgrades or with a tailwind. I tried Tow/Haul for a while and didn't see much of a difference in behavior, so I didn't really worry about it.
That said, when I got off the interstate and started running country roads with stop signs, state highways with stop lights, passing through small towns, etc.—then I engaged Tow/Haul all the time. The engine braking assist was fantastic, especially in less-than-ideal weather conditions. And the shift pattern just makes more sense in stop-and-go conditions.