According to the 2014 Trailer Life Tow Ratings, a 4x4, F350 CC SRW with a 6.2 gas engine has a tow rating of only 12,000 lbs with a 3.73:1 (not big enough to pull your 14,000 lbs trailer; or 15,000 lbs with a 4.30:1 rear end gear ratio. The diesel will have a larger pulling capacity with any of the offered rear end gear ratios. And if you go DRW, the tow rating gets MASSIVE. I could not find the 2015 ratings. I prefer a gasser for many of the reasons mlt22 gives, but with that trailer weight, I would go the diesel.
From http://www.trailerlife.com/trailer-towing-guides/
F-350 CC SRW 4WD 6.2L V-8 12,000 (i)
F-350 CC SRW 4WD 6.2L V-8 15,000 (l)
F-350 CC SRW 4WD 6.7L V-8 TD 15,900 (f/h)
F-350 CC DRW 2WD 6.2L V-8 12,400 (i)
F-350 CC DRW 2WD 6.2L V-8 15,400 (l)
F-350 CC DRW 2WD 6.7L V-8 TD 22,600 (i)
F-350 CC DRW 4WD 6.2L V-8 12,100 (i)
F-350 CC DRW 4WD 6.2L V-8 15,000 (l)
F-350 CC DRW 4WD 6.7L V-8 TD 22,800 (i)