Sway bars work by linking both sides of the suspension. So theoretically, the car will squat slightly instead of roll/lean because the the arms are attached.
I use sway bars on carpet with foams because traction is not an issue and chassis roll is.
Example, I was using the front only to reduce steering a bit. About mid turn I noticed one rear wheel coming up and slipping. I added the rear sway bar to decrease chassis roll and as a result, both rears stayed planted.
I don't think there is much need unless traction is high.