Once you add some basic handling mods such as lowering springs, upgraded struts, better tires, etc, it becomes increasingly important to consider upgrading your sway bars. As you improve the ability of your car to stick to the road, you will notice an increase in body roll (or sway/lean). This is where a stiffer/larger sway bar setup becomes beneficial. Sway bars work by distributing the upward/downward force of the car evenly from left to right, in an attempt to keep the car level (eliminate the heavy lean, or body roll while turning) the factory sway bars are sufficient for a factory suspension/tire setup, but once you change things out, they are no longer enough. This is where the larger diameter/stiffer sway bars come in, they will help keep all 4 tires planted firmly on the pavement, and drastically improve your cars handling ability.

Ours is 1.28" in diameter.

Sway bar 101: This is assuming you have a properly setup front/rear spring rate and good shocks/struts...  For example, lets say you are coming into a corner fast and want to make the turn.  If the car tends to understeer (front pushes/does not turn) you will want to increase the rear sway bar stiffness.  People generally prefer oversteer (rear swings out) in a corner in a front wheel drive car because you can always accelerate out to control the amount of oversteer.  If the car oversteers a lot, then increase the front sway bar.