I have got an 05 crew cab 2500HD with the 6.0l and with a 8500 lb camper behind it I would see about 8 to 9 mile per gallons and with a 26 ft v nose steel snowmobile trailer with little cargo I got about 9 miles and with a 24 ft enclosed car hauler weighing in at about 3500 lbs doing 75 i got about 9 miles per gallon.
With all these at light to heavy I got about 8 to 9 miles per gallon. But with all these I could easiler do 75 and when I wanted to go just put the pedel down and off you went. I have used an Avalanche with the 5.3 on the same camper and it would only get about 8 miles per gallons but the 6.0l made for a better towing engine with the power it had. You were not reving out to 5,000rpms and it did not take miles to get up to speed like with the 5.3.
So if you are looking to tow I would say the 6.0l over the 5.3. I have not experience with an 8.1 so I will not coment on that.
Also with my 6.0l i get between 12.5 to 14 mpg unloaded highway depending on time of year. Also my truck has 4.10 gearing.