Pulled a 29' Sunline for 10 years with Dodge 3500 and Hensley hitch and never had even a hint of sway. I've pulled the Minnie with the Tundra and Equalizer hitch and haven't had a hint of sway and I've towed it over 5,000 miles.
At the same time, I believe that you have to watch your weight distribution and make sure the hitch is properly set up. I've seen rigs going down the highway with the trailer higher at the hitch which is a recipe for disaster. Also, the design of a trailer may have an impact. It's worth the time and effort to take a rig and get it weighed and know whether you're overloaded or the hitch weight is below the recommended percentage.