If we're gonna revive this thread, might as well do it right. Here are my 8.1 observations.
I have towed a bit with my Avy 2500, from Wyoming to Arkansas, in Montana, and a few trips in between Colorado and Wyoming. The heaviest I towed was 18800 lbs which is right at the GCWR for an Avalanche 2500 (with 4.10 gears; ones with 3.73 gears only have a GCWR of 17000 lbs). With that load, I towed from Arkansas to Wyoming, climbing up to 8100 ft at the highest, with several climbs and descents in elevation in-between. My fuel economy for that haul was around 6 MPG. It held 55-60 on the steepest part, pedal to the floor. If I had the lower gears, I think it would have done even better.
GCWR: 16,270 lbs
GCWR 16,200 lbs
I now have a K2 2500HD with the 6.0, but have not hauled with it yet.
Empty the 8.1L does similar in the mountains in between Laramie and Denver. I have made the trip numerous times in each, under similar conditions and the gas mileage (hand calculated over several similar trips) is slightly better with the 8.1 vs the 6.0 (14 mpg average vs 13.5 mpg average). I do have 285 70 r17 tires on the 2500HD, so that does hurt the comparison, but overall, the 8.1 has plenty of torque that it just climbs up without the need to shift and up the revs.
Around town, I get around 9.5 in each. So for me and my driving style, there is no significant difference in fuel mileage between the two. And in the mountains and/or towing I enjoy the torque of the 8.1.