I had an '05 Burb and a 30 ft, 7200 lb travel trailer. I had to get a ProPride hitch to get the sway under control. On the plus side it had very comfortable seats, which I still miss. It was very comfortable on a long trip. As with any gasser expect to be running high rpm's in the mountains (4600 was common). My DW didn't really care for that, which is part of the reason we will be getting a diesel down the road.
Some things to consider: Gas usage as you know is a big negative. If gas prices go back up, will you be willing to pay the price? Parts can be expensive. As an example our Burb had electronic shocks in the rear, which went for $550 each at the time. Leaking oil cooler lines are a common problem. Be sure to check these as well as the transmission cooler lines when shopping for one. The oil cooler is inside the radiator by the way.
I guess the bottom line here is that a Suburban with an 8.1 is a great tow vehicle, but expect to sink cash into it and be prepared to fill that 39 gallon fuel tank at least a couple times a day on a road trip.
