Tough decision... The LC will be a lot easier on the kidneys once you hit the destination, while the F-350 will provide an easier tow, but not as friendly when 4x4-ing it.
In that situation, I'd check with the dealer to see if the LC can handle the towing (perhaps making sure you have a transmission cooler), and go with the LC. I'd have to be careful with towing, especially at higher elevations... but once the rig is in place, bouncing around the terrain in a true off-road vehicle will be a lot more fun. Life is short... might as well use the LC to its fullest on a month long vacation.