Pskhaat,
I think everybody has covered the basics. I've got 10's of thousands of miles behind the wheel of 6.0 & 6.4L SD's, primarily highway but some dirt - here's my bullet points.
6.0's had issues up until about 2005. By 2005 the turbo had been redesigned, and seems fairly robust - these are 250,000 - 300,000 mile engines, so the long term jury may still be out - but I would have no problem taking a very long journey with an '05 or newer 6.0.
There is no question that the front coils ride better, handle better, turn sharper and are just better in every way to the leaf spring front ends, so in my opinion keep your search to 05's an newer.
The 6.4 (2008 and newer, but Ford launched model year '08 in January of '07, so there are a lot of them on the road) is a fantastic engine. Huge improvement over the 6.0 in all but 2 ways. Its quiet, its fast, very nice to drive.
Downsides
1) Fuel mileage. An F550 with a load of about 10-11,000 pounds on the back that would return mileage of 12-14 on the highway with the 6.0 will probably get 8-10 in the 6.4 (these are my personal experience numbers, YMMV) Installing a Banks kit will solve this issue and give you way too much torque and HP, so many people go that way. A very reputable Ford tech I know once told me that if he could convince people to keep their Banks kits on the lower settings, he would recommend them to everyone.
2) Requires ULSD fuel. No problem if you're staying in North America, and increasingly available in Mexico, but a serious problem if you can only find LSD (low sulphur diesel people, not the other

). Its not that the engine will run rough, or smoke, it just won't run. You'll clog your particle filter very quickly. There are rumours that you can just cut the filter out of the exhaust system, but there are so many sensors and things on modern engines, I would be hesitant to do that.
edit - I thought of one other potential drawback for overlanding. When the engine is undergoing it's "regen" phase on the 6.4's the exhaust is incredibly hot. Hot enough that I would pay very close attention to the plant life around my exhaust pipe when I parked. They don't actually blow flames out, as some internet rumours would have you believe, but they might as well, hot as they are.
One comment I haven't seen: I love driving manual transmissions, but in a heavy vehicle with a heavy load, kids screaming, dog panting, etc..... I'm a big fan of the Ford Torque Shift auto. Tow/haul mode will engine brake for you, it adapts to your driving style, in my opinion its one of the unsung heros of the SD line up.
Anyway, that's my opinion.
-Matt