The 3.6 started in 2011. Rated at 290 HP and 260 ft/lbs torque. By comparison, the 5.7s run anywhere from 350 to 400 HP depending on year and trim, and 390 or more ft/lbs torque.
While the numbers are both suitable for towing, there are differences in ability to deliver that power. The 3.6 is revvy and max power is achieved high in the RPM range.
In my opinion (and I have both engines) it is a trade off. Better gas mileage can be achieved daily in the 3.6, but for towing, I'm not even considering using my Jeep. The truck with the 5.7 is just easier all around and is meant for heavy duty work. Yes, the mileage is a cost, but in the long run wear and tear will be less. So, cost savings.
As for the OP, he is only towing 20 miles or so, so I think the 3.6 would be plenty for that type of work.