Excursions with the Powerstroke command a premium that, IMHO, is not worth it.
The 2003-2006 Suburban 2500s were absolute beasts - huge payload and huge towing - but the 8.1 models are hard to find, and tend to be a bit pricey relative to blue book price. This is probably your best choice.
The 2007-2013 Suburban is great, but it's hamstrung by the weak receiver, and relatively low GCWR. My receiver is rated at 500dw/1000wd lbs of tongue weight, And with a curb weight of 6500 lbs, that 14,000-lb GCWR looks pretty small.
Now, that being said, we took my '08 out to the Grand Canyon and Colorado, including a drive through the Eisenhower Tunnel. Our trailer is ~6500 lbs, and I have a family of 5 which includes three teenagers. My family weighs ~900 lbs.
The Suburban pulls it just fine, and I'm always relaxed behind the wheel. We towed over 5000 miles in two and a half weeks.
You can click the link in my sig to see our rig.
Here's the weigh slip from that trip - note that I'm right at my 8600 GVWR limit, and I'm over on my GCWR:
