Sway bars: AKA an anti-roll or stabilizer bar is a torsion device that resists the leaning action of your ride upon taking a corner. The stiffer or stronger this bar, the less lean you will experience on said corner. This lean is often referred to as body roll and is a necessary "evil" to the street car. Without it, you would likely be in constant upset of the cars balance and be hard pressed to drive confidently fast around your average corner on the street. The sway bar responds to body roll in much the same way as your springs, but with at least one fundamental difference. If one is going straight down a road and hits a rut or bump perpendicular across the road, the sway bar offers no resistance or change in ride quality. If this bump is one wheel only, the sway bar will apply force to that wheel and attempt its return to un-loaded or neutral position. The sway bar can be seen as a compomise between softer springs for a comfortable ride and heavier springs for decreased body roll.
Griggs front anti-roll bar:
This is a major design improvement over the traditional front sway bar of the Mustang. This has all spherical joints and eliminates the suspension bind created when the bar is put under load. This bar requires some welding to the cars frame and will add some NVH to your cars ride. See Griggs Anti-roll bar description.
The rear sway bar is often replaced with a heavier one due to inhearant understeer in the Mustang. I have chosen to run an adjustable rear sway bar for the ability to address understeer in very aggressive driving I do at AX events. This bar installs much differently than the stock one and begins with a "base" stiffness of 1~7 and will have 3 additional settings beyond it.
Ultimately, the sway bar is really a tuning device to address understeer/oversteer conditions. As such, one bar is NOT for every situation and don't recommend one just install a heavier sway bar in the effort to improve ones handling. This should really be the final step in setting up good balance in your cars ability to take a corner.