The trailer swinging horizontally is sway. The trailer pitching fore and aft (vertically at the hitch) is porpoising. There is no hitch today, including the Hensley and Pullrite, that addresses porpoising. The spring bars do not damp porpoising or eliminate its lever arm on the tow vehicle. While they may oppose that motion in one direction, they contribute to it in the other. Porpoising is addressed by shock absorbers on the trailer, and by adding axles to it, which lenghtens its base on the road.
All towed vehicles, including fivers and semi trailers, have the potential to swing behind their pivot point. This is generally not referred to as sway, and most consider fivers and semis are considered not to have sway, even though anyone's who's spent time on the highway has seen them swinging behind the tow vehcile. What's generally referred to as sway is the swinging or oscillation behind the tow vehicle that increases in magnitude unless something like manually braking the trailer and accelerating the tow vehicle is done to reduce it.
The problem with sway, with a conventional trailer hitch, is that it steers the tow vehicle from the rear, by yawing it, in the opposite direction of the trailer, using the lever arm of the rear axle to ball distance. What sway does to the tow vehicle in this manner is the same as the driver yanking the steering wheel back and forth. This, in turn, increases the magnitude of the trailer sway.
A conventional sway control can only oppose the steering effect of sway as much as it opposes the steering effect of the driver. In other words, in order for the tow vehicle to be able to turn the rig without the sway control binding, its damping, or opposition, to sway has to be significantly limited also. At best, it can reduce sway and slow down the rate at which severe sway increases in magnitude.
A Hensley or Pullrite doesn't just attempt to fight sway. It totally disarms it my removing its weapon against the tow vehicle, the lever arm of the rear axle to ball distance. Sway cannot yaw the tow vehicle of a Hensley or Pullrite equipped trailer anymore than it can yaw the tow vehicle of a fiver. While these may wiggle a bit, there's no reinforcing feedback from the tow vehicle, hence there's no increasing oscillation.
The reason you see semis and fifth wheels overturned isn't because of sway. It's because of the high center of gravity, and the greater side (sail) area and the higher center of wind pressure. The much lower trailer's handling (especially in emergency manuvers and curves) and vulnerability to wind (even when parked) is actually better than a fivers or a semis.
I've gotten to the point of not even comparing the Hensley to the Pullrite, because the differences pale in comparison to the difference between them and anything else. I'd rather see a new owner with either than something much less.