Tow ratings for 2009+ GM SUVs are low 5000 pound range, high 5000, or near 8000 depending on options and equipment. They all come with the same receiver with 1000 pound rating and 7-pin wiring. The frame is the same. Same 5.3L V8 and 6-spd trans. The springs, tires, maybe shocks are the same. The difference is axle ratio (low 5000 to high 5000 pound tow ratings) and the HD trailering equipment package (high 5000 to 8000). Start by verifying what equipment you have. Open the glove box and find RPO sticker with as built equipment. It looks like this:

You will have either GU4 (3.08 axle) or GU6 (3.42 axle). You may have Z82 (HD Trailering Package) or not. From that, you can determine your actual tow rating.
The big one is the Z82, and specifically included with it is the upgraded transmission cooler which I believe is very important to towing any high walled trailer. Should yours not have that, they can be added by a competent transmission shop for under $500. The main part itself is about $50. I would not worry much about the difference between 3.08 axle and 3.42. The 6-spd transmission really helps compared to trucks from 10 years ago. Use tow/haul mode and M4 to prevent the truck's engine from getting bogged down and shifting too frequently.