Ya can't compare an H2 to a 2500 Avalanche. Yes, they share some parts, but the 2500 is beefier from frame to axles to brakes to tranny to factory tires to engine.
Well, I guess you can compare the gas mileage.
Drive one, or the very similar 2500 Suburban (w/ 8.1L). All of the 2500 Avalanches have 8.1L engines. Some 2500 Suburbans have the 6.0L similar to the H2. The torque curve of the 6.0 is very steep, meaning to tow you have to have that thing revved high. The torque curve on the 8.1L is much more suited for towing, making a max of 455 lb ft. The HP on most of the 6.0L GMs is around 345. The HP on all of the 8.1L GMs is 340.
Make sure to check the option codes for these two figures:
GT4 = 3.73 rear end
GT5 = 4.10 rear end
You want 4.10 no matter what for the towing/frequency you are describing.
Definately buy a 4wd, whatever you purchase.