This is all IMO:
As I understand it...
The Hayes unit applies all trailer brakes at the same time to counteract sway.
The Jayco unit applies trailer brakes only 1 side at a time to counteract sway.
Both units are designed to prevent catastrophic loss of control... just before the 'excrement hits the air movement device' (aka SHTF). But neither unit does anything to stop/dampen the initial 'wiggle'. If they reacted to initial 'wiggles', for some (many?) they might accelerate trailer brake wear.
Trailer hitch anti-sway devices are friction devices intended to begin dampening/stopping the initial 'wiggle' well before things get out of control. These devices also help keep the rig straight on the road from the 'push' of passing trucks, crosswinds, etc. By doing that, the hitch anti-sway devices also tend to reduce many uncomfortable 'white knuckle' drives.
With the current technology (as I understand it) the Jayco and Hayes units can be added as an additional safety measure. I haven't seen evidence they are a substitute for trailer hitch anti-sway devices.
(These are my opinions and worth every cent you paid for them.