Go with the 350.
Don't make the mistake of forgetting Payload and only looking at towing capacity.
The trailer you are looking at has a GVWR of 12,200 lbs. That's about 2,200 lbs of pin weight...then there's the hitch and passengers, etc. all count against you PAYLOAD rating....go with the F350.
"If we couldn't laugh we would all go insane."
Arctic Fox 25Y
GMC Duramax
Blue Ox SwayPro