I towed with my 2011 for a number of years. Never pushed its 6500 lbs limit, just mostly our event trailer going to events around the country. 16' single axle aluminum box trailer, about 3,000lbs all in. I found the 4.6 did fine overall and would never hesitate using it to tow a medium tow need with. With the truck being fully built including an ICON Stage 6 suspension, I very much appreciated the KDSS system. Normally a built truck on 34"s can be a bit spongy in the corners or be pushed around by side winds hitting the trailer. The KDSS takes over and keeps the truck rather tame, when others would get sporty. Like all modern Toyotas as soon as you plug a trailer in, I swear its like the computer goes "oh we are towing so who cares about the MPG." Mileage drops.
Not the 460 but just towed with our 470 to and from Overland Expo in AZ, same trailer. The lower torque of the 4.7 is noticeable, but the higher revving HP of the 4.6 stands out. However on the HW on a long cruise the 460 is hands down the machine of choice between the two.
Just sold my LX570, great truck and yes with that 5.7 it was a beast towing, but you pay for it deeply in the fuel milage about 4 mpg worse than the 460 towing the same trailer. BUT the 570 will let you go up any hill as fast as you are willing to try.
For baseline our shop has our trusty Ford RWD 7.3 diesel, is a towing machine that does not care what its behind it. Used this for years taking my FJ40 then FJC to events.