Just recently upgraded from a 2001 F150 5.4 to a 2013 F250 6.2 gas. We tow at Rockwood 8313SS and the dry weight is around what you are towing. Our F150 did ok but we wanted more cargo wiggle room so we looked at new F150 and F250 and ended up with a new F250 less than what we would pay for a F150 that would tow our trailer.
You can look at the F150 EB with the max tow package but those are harder to find and like I said was more expensive the the F250.
We looked for about 3 months at many different vehichles, Tundra, F150 EB (max tow), F150, F250 and even looked at a F150 that had the 6.2L in it.
Glad we went with the F250, love it towing and never looked backed.