To the OP, when you say sway, do you mean a back and forth oscillation? Or do you mean the wind and passing vehicles pushes you around a little? The first is what I would call sway, the 2nd is more normal and will be reduced by a more HD vehicle or a better sway control device. If you have a back and forth oscillation that gets worse with speed and seems unrelated to other influences such as wind or passing vehicles, you need to get that fixed first, which is usually caused by too light of tongue weight. It can be dangerous and you need to fix it.
Clarify what you mean by sway, and you can be better helped by the others here.
The Equalizer is still around and a good hitch, I have not used one. As was already mentioned, your Reese system could possibly be converted to the Reese Dual Cam system, which is also very good. That is what I use. The one thing I don't like about the Reese system is the way the cam arms mount to the trailer frame. It is a poor design and many have issues with it. I had to reinforce mine, I also had to start using Vaseline on the cams with my new heavier trailer. It works great now. Even when I was having an issue with the mounts, the trailer tracked really well behind my Suburban.