I dont know too much about the 6.5 detroits, everything I've read and heard says they're reasonably reliable but anemic in the power department. I'm obviously biased towards a duramax (go figure) but If I was in your shoes with your budget looking for a work truck I would get into an LB7 duramax before a 6.5 any day of the week. I'm not sure where you live but in my neck of the woods (Wisconsin) decent higher mileage LB7's can be had for around $4000.
2015.5 GMC Sierra 2500HD Denali LML Duramax
2007.5 Silverado 2500HD LTZ CCSB LMM Duramax - Triple Black (SOLD)
2008 Silverado 1500 LT 5.3 CCSB AFM Deleted - Olympic White (SOLD)