I agree with those who say the F-150 is not enough truck for an 11,000# GVWR trailer. I know the brochures say that it will tow that much, but you will run out of payload long before you get there.
My XLT has a payload of 1,895#. Take out 400# for me and DW, and you have a remaining payload of 1,495#. Put a 100# WD hitch on there and a couple of hundred pounds of general stuff in the bed of the truck, and you are now down to 1,195# of remaining payload. I like to keep my tongue weight in the 12% to 15% range, and use the 15% number for doing workups. At a 15% tongue weight with an 1,195# payload remaining, you are limited to a trailer with an 8,000# GVWR. Even using the 12% figure, you have a trailer limit of 10,000# GVWR, and I consider that pushing it to the extreme. Getting the HDPP package will help by increasing your payload.
To tow a trailer with a GVWR of 11,000#, I strongly suggest at least an F-250.
ON EDIT: Since it was the engine you actually asked about, the 3.5l EcoBoost has enough power to pull that load, the 3.5l naturally aspirated does not. Given the choice between the 3.5l EcoBoost and the V8, I would choose the 3.5l EcoBoost.