I had a 2007 F350 6.0 that I towed my 35' 5er about 15,000 miles with. Traded it for a 2012 F350 6.7 at about 84,000 miles. Not because I had problems with the 6.0, just that I made the mistake of browsing the new truck lot when in for normal service.
Only problem I had with the 6.0 was a failed cam sensor at about 54,000 miles, fixed under warranty. Otherwise never a problem and towed great.
Friend had a 2003 6.0 that did have problems. One Ford service department replaced the turbo twice before another Ford dealer figured out it was actually injector problems.