Here's feedback from the very happy owner of Big Duke, my 06 F350, KR/CC/LB/dually, exactly what you're looking at.
This has been without a doubt the best, the most capable, and the most comfortable truck I've ever owned. I just love it. I've moved a neighbor's backhoe with it, crossed a mountain on a 1 1/2 lane country road with over two tons of cut red oak in the bed, it never broke a sweat. Started it at zero degrees a few weeks ago without being plugged in, that was impressive. And it rides nicer than most 3/4 ton trucks. It did blow a HPOP seal at 94k, fixed under warranty. Otherwise, it's been regular oil changes with Rotella T5 and T6, with Ford oil and air filters (aftermarket filters aren't as good), and no problems.
The 5R110 auto trans is as bulletproof as they can be made, very rare to hear of any problems with it. You'd have to do something really dumb to hurt the Dana 80 rear axle. One drivetrain issue: The auto 4x4 hubs can get cracks in the vacuum actuator line, or some times the vacuum valve goes bad. If that happens, spend some time and/or money to get it fixed, or just get out and lock the hubs manually when you need 4x4.
You can get the 'death shake', bad shaking of the front end when you hit a bump in a turn. Mine had this when I got it, the problem went away when I put on new tires about a year ago, and hasn't come back.
The engine: to make it reliable for the situation you're in, you should do two things:
Flush out the cooling system with a descaler, and put in a non silicate based coolant. Ask in the 6.0 forum for the details on this. Under heavy loads and extended high heat, the silicate based Ford coolant can scale up and clog the EGR and oil coolers. Doesn't happen overnight, but it does happen. You can get an external oil cooler from BPD that also solves the scaling issue, but it's not cheap, around $1500 just for the parts I believe.
Change to a synthetic oil. I'm particularly pleased with the new Rotella T6. Starts easier in the winter, and it seems to have eliminated the 'stiction' that was just beginning to show up (injectors sticking at idle from deposits).
What you should not do:
Replace the head bolts with studs, unless you like spending a lot of money for no good reason. In stock engine form (see next), the head bolts are fine.
Mod it for more power. When I see a posting here on a troubled 6.0 that's 05 or newer, there is almost always a bunch of power mods listed in the signature. The 6.0 is already a hot engine, it makes 30% more HP than a 7.3, with 25% less displacement. Push it further, you can start breaking expensive things. What I do know is two people who have gotten 180k+ reliable miles out of 05 and 06 6.0's. In both cases, the engine was left in stock form.
6.0's can be reliably modded to 400+hp, but it costs a lot of money to do it right, and even more if it's done wrong and you blow a head gasket. You already have enough power to pull a 13k trailer.
You can strip off the EGR cooler, but that's not a simple task and the computer will throw a code. I left mine alone, and get 14-18mpg if I don't leadfoot it.