JMO but if that's all you tow I'd go 250/2500 gas. You'll get 3000+lbs for payload even in the upper trim levels. You'll save $9,000 over the diesel.
BTDT on with a 2010 F150 to a 2012 Ram 2500 CTD. IMO it's wasn't so much the jump from the 5.4 to the CTD but the jump from the 1/2 ton to the 3/4 ton part. I was towing a 31' 72-7300lb loaded TT. My F150 was maxed out also. I was right at the RAWR.
The biggest difference was in the handling department. The 3/4 ton flat out gives a more stable platform. Wind gust and other factors that caused the truck and TT to drift a bit just didn't happen when I moved up to a 3/4 ton.
Just me but if I was only towing 6000lbs I would get the nicest gasser I could. We have gone to a 5th wheel now and that's why we went with the diesel. I live in Oregon and have lots of hills and mtns to travel over. The diesel does make it easier but in reality I still get to the same place at the same time as before with a gasser.