The NNBS trucks have the oil consumption issue too. I believe it is caused by the cylinder deactivation generating heat. The Tahoe in my sig was K.I.A. in September due to this problem, standing me and my family in Laramie, WY. The truck only had 95k miles, but was out of warranty due to age. GM is well aware of this problem and still didn't want to step up even tough I had over a half dozen entries in my oil consumption test log given to me by my dealer in Virginia. My advice is to find a tuner (such as BlackBear on this forum) and have cylinder deactivation removed. It will affect your mpg, but I believe it will save your engine.
Also, there is an issue with the dash cracking on the left of drivers info hump or near the passenger airbag. My truck also had this problem. Again, GM is very aware of this but still does what it can to avoid paying for using cheap plastic. Only thing I can say is to pretend it doesn't exist should it happen to you.
Check the towing ratings on the truck. It seems like the 5.3 lost 1 ton of towing capacity when the 6-speed was introduced (based on owning a 2007 and comparing it to a 2013 last week). I'd consider going with a Denali because it has a 6.2. The numbers for that seem to put it in the 7000-8000 # towing range.
Regardless of what engine you go with, get cylinder deactivation removed.
I like the new Durangos over the 2nd gen, but not as much as the 1st gen. The 3rd gen looks to be a worthy contender to the Tahoe and Yukon. The things that make me any away from it are its newness. The Tahoe and Yukon are older with 20+ years of improving the same tech. The setup of the new Durango is very new with the exception of the engine. Speaking of the engine. I've heard of numerous problems with the heads warping. I've also seen freeze plugs falling out. I also dislike 2 spark plugs per cylinder. They are copper, but good luck replacing them for under $100 total in your driveway. You'll pay a lot more at a shop.
Overall, I'd still go with the Tahoe/Yukon, unless you are also looking at the Audi Q7. That thing is impressive. You can get a supercharged V6 that pumps out 330bhp our even a diesel. It's a crossover, but it'll tow 8,000 lbs. and achieve decent mpg with its 8 speed trans. It also happens to be in the price range of well equipped Tahoes and Yukons, especially the Denali.