Make sure you adjust your height accordingly to level when attached to your truck. You will also find at least in my situation that I had to add a step to our folding steps {kind of border line, but wife is short}. Our trailer came with it lifted which is great for dry camping in the woods {and sloped driveways}. I really can't answer honestly about swaying or any other differences as the trailer was already lifted when I bought it. But my dually does just fine with it {and it sits level}. Been across the country several times. I don't think you will have any problems maybe someone else will jump in to verify.
2003 Sandpiper 32 ft., 2006 Dodge dually Big Horn, 4X4, Cummins H.O., 6 speed, jake exhaust brake, Edge Tuner , turbo timer, AFE stage II intake, S.B. clutch, Toyo Open Country Tuff Duty tires, KF7/AQD-SAR139