Isn't the engine 4.2L (no eco-boost available yet), not 3.7?
My experience, FWIW:
Our 1st TT was 20' and 5K lbs (scaled weight) and we towed it with a 2000 F150 with the 4.2L V6 and 3.55 gears (and added a tow package). The max. tow capacity was 5500 or 5800 lbs (can't recall exactly). It was slooow to accelerate, super slooow on hills and difficult to maintain a steady speed in heavier gusting winds. On steeper grades, like Grants Pass in Or., we could only make 30-35 mph
flat out and had to run on the right shoulder along with the semis. Not a fun experience.
Besides being slow, it was hard on the drivetrain and the engine was running at high rpms a lot of the time to make enough power. On an 1800 mile trip to NoCal and back, we had to stop at a Ford dealership 3 times to get some engine work done (nothing serious fortunately - we babied the truck and it was in excellent shape). Gas mileage was awful too and as low as 5.7 mpg on one run on the above trip in the hills. No problems whatsoever with handling and sway. When we sold the truck last year (at just over 100K miles on odo.) to a co-worker of DW, they had to get the tranny rebuilt a year after owning it.
An excerpt from
this article for the '08 F150 says:
The V6 engine, says Consumer Guide, has "adequate power for commuter duty, but struggles with even modest loads." Kelley Blue Book calls the engine "tepid but fuel-efficient (for a big truck)," but cautions, "We don't recommend this engine for towing or hauling heavy loads." That certainly was my experience... I would say for shorter local trips on flat-ish roads, you'll be okay. As mentioned above, I would restrict weight to around 4500 lbs.
This was one of our trips to the dealership mentioned above. You don't want to end up like this, lol. Another camping day lost, sigh...
When we bought a longer and heavier TT, we moved up to a "real" truck. No more towing issues, hehe...