Sway is a strange phenomenon, I rented a 25 footer with an equalizer hitch and I purchased a 25 footer with a Blue Ox hitch. Both weighted bout 5000 lbs. dry and neither had any problem with sway.
The first was pulled by an F-150 the second with an F-150 4x4 with a higher center of gravity. Both were rock steady and recovered nicely from truck and wind buffets.
Others people seem to have endless problems with sway. I suppose you will just have to see what you rig does.
Our first few trips we opted for pull through camping spots, but with a good spotter and practice it is not hard.