The 6.0L was, overall, a decent engine. They make WAY more power than the 6.2L/6.5L GMs and are more reliable as well. They are not *as reliable* as the 7.3L and that caused a lot of problems.
How are they not as reliable? The main factor is the added electrical complexity for emissions reasons, we are not going to get away from electronics on diesels, but they get better every year! The bigger "problem" came not from the engine itself, but the fact that LOTS of owners were used to achieving 50% power increases with the 7.3L PSDs w/o any engine problems at all! Well, the 6.0L does NOT appreciate "hop up" parts or tuning, not one bit ad they bite hard when you try to get more power from them. Stock, they are GREAT.
I have been working on and with the 6.0L (same as the VT365 in an International) since they first came out and have YET to see a blown HG with my own eyes. I have no doubts that an engine or two has failed a HG, I just have not seen one myself. That is not to say I have not seen engines with the heads off for HG replacement, it's just that the tech couldn't SHOW me where it/they was leaking or failed.
EGR coolers are a problem and the most common cause of HG replacements BY FAR. When the EGR cooler fails you get exhaust gasses in the cooling system (dye tests fail indicating "combusion gasses in coolant" which are incorrectly assumed to be because of a HG or cracked head). The EGR coolers are fed out of the oil cooler, which has small coolant passages. Dirt and debris can clog the oil cooler on the coolant side restricting flow to the EGR cooler causing it to overheat and fail.
If you want your 6.0L to "live long and prosper", do not tune it or install "hop up" parts of ANY kind and keep your fluids in good condition.
PS: Change BOTH fuel filters at EVERY service!