It really depends on how heavy you are towing. I tow all over the mountains on the West Coast with my 6.0. But loaded gross weight I am just under or right at 16,000lbs.
If you are towing at max weight on the Ike everyday at 11,000 feet you are going to get a diesel. If you are not and under 10,000 you probably don't need it.
The New Chevy 6.6 looked promising until GM put the 6 speed and 3.73s behind it. Towing with similar weights my 2017 6.0 6 speed with 4.10s posted similar times. The 6.6 needs at least an 8 speed and 4.10 gears.