Without being too pro or con I will try to give you good information in this reply. It is easy to slide into, "This is my truck and it's the best!" Feel free to PM me about it.
The 6.0 diesel is well documented. You can find tons of information on them at ford-trucks dot com. They have their own forum there and it is where most 6.0 owners hang. I work on my own motor and have enough info gleaned from the web that I can do almost all my own work on it. Often I choose not to, but I am armed with enough info I can keep the mechanics honest.
The 6.0 motor was introduced in 2003 and had significant problems that led to a poor reputation for durability. Most of these can be addressed by owners with repairs and upgrades. In the end most either love 'em or hate 'em. I really like my truck -- it has 180K and I expect it to go another 150K at least. That said, it is probably not a truck for those that have no access to a shop familiar to 6.0's or those who don't want to perform maintenance themselves. It is also a motor that requires monitoring for best results -- I use an iPhone app to watch my motor's vitals. This may not be something that you are interested in doing.
If the truck is available at a really good price (many 6.0's are great bargains because of the stigma) and has had specific upgrades/repairs done it can be a dependable vehicle. However, there are those who have had the truck and would never own another. Your outcome with this truck entirely depends on its maintenance record and condition of the motor, along with installing any proactive upgrades needed. Beware the 6.0 that has been chipped and run really hot and hard. They are tough but they do not like to overheat. The best scenario would be a motor that has been "Bulletproofed" and run with regular maintenance. Fluid changes including coolant are critical.
At issue with the 6.0 motor is its design that relies on an EGR cooler and an oil cooler that can cause problems that cascade to injector, turbo, or head gasket failure if not caught in time. Additionally, the 2003-2004 years had a weakness in the high-pressure oil pump. There are after market parts and delete kits available to address these problems, but these are not inexpensive repairs. I have spent almost $5000 over the life of my truck on this work, but about one third was labor costs. I don't find this excessive considering its age (eleven years). And it runs so well now : )
As far as routine maintenance, the 6.0 is a breeze to change oil, gas filters, and there is plenty of space under the hood to do the work compared to late model nightmares. I appreciate not having to worry about DEF fluid and exhaust systems that cost as much as another car. Trucks are getting so expensive they are requiring first borns as down payments!
Most folks simply avoid this motor and go with another. That's why 6.0's are easier to find and harder to sell. The older 7.3 is well regarded as is the gas V10.