I've got a 2011 Avalanche I'm using to pull my 25RR. It pulls fine but don't expect to break any speed records. I usually try to keep it around 65 mph to help the mileage. Towed it from Ohio to Arizona about 4 weeks ago and averaged about 8.5 mpg on the 2200+ mile trip.
Mine is equipped with a 5.3, trailer towing package, automatic load leveling (air)shocks and I'm using a Blue Ox weight distribution/anti sway hitch.
One note on hooking up with the load leveling shocks - hook up with the truck off. Get your hitch set up, leveled, and adjusted, then let the tow vehicle shocks do their thing. Blue Ox says to disable any load leveling system while using their hitch. My Avalanche does not allow you to disable the system so turning the truck off while getting the weight distribution system set up solves the problem.