I have owned the 2003 body style and my 2011 2500HD has a similar front to the current gen.
With the Tahoe, you are going to take a lot more $$ to make it off road capable. Sure it is body on frame, but the bumpers have to go at minimum. With the LR3, find one with 18"s add a $200 lift rods and you are done.
I like my suburban much better than the Tahoe. With the 3rd row seating (non-fold flat as mentioned) you have zero cargo room. On the other hand, the Suburban is a solid tow-capable LWB expedition platform, the Tahoe is just...as another poster stated: big. All of the girth of the Suburban, but without the utility.
After owning both, I tell people Chevy designed the Tahoe for people who won't be caught dead in a suburban to buy one, and then 3 years later trade it in on a suburban when they find out it is really what they needed.
As for the engines, I can't say much about the modern displacement-on-demand, but the old 5.3 is reliable, easy, and cheap to work on. The maintenance of living with a Tahoe is going to be much cheaper than and LR3.
But if you really want to wheel, the LR3 is the way to go. If you just want to tow in comfort, the Tahoe is probably a better buy, if you want a wagon that can tow and haul things in the back, you need to look to a Suburban.
I like the new 4-Runners, but I wasn't impressed with their towing capability. My next rig/trailer tower will most likely be an L322 or an LR3/4.