We also have a WJ 3006wk and it is towed with a 2010 Dodge 2500 Diesel 4x4 and 1000lb Equalizer WDH. I have had no issues with sway on the three towing experiences so far. I was worried before I first picked it up but I had big rigs going by me and didn't feel anything at all. I have no comparisons to give since it has only been towed by that truck.
2016 Windjammer 3006WK
2010 Dodge Ram 2500, 4x4, Diesel, Front Hitch, Air Lift 5000 Rear Air Bags.
Equalizer E4 1.4k/14k WD Hitch.
TST 507 TPMS
Furrion FOS48TA Observation Camera
Garmin RV-760 GPS