Your stock sway bars are designed to work with the stock suspension.
That doesn't mean that the stock bars are
the optimal ones for you.
Remember, engineers aren't the only people that designed our cars. Lawyers, bean counters, etc have influenced the design as well. And usually for the worse, from a performance point of view.
Now here's my theory...although I'm sure someone came up with it before me:
You will notice a difference running different sized bars,
as long as the rest of the suspension remains unchanged.
For example, if install a 20mm rear bar, but keep stock springs, you'll get
X amount of oversteer.
Now, if you install a set of coilovers with higher rate springs, and keep the 20mm rear bar, you'll get
X-y amount of oversteer.
This is due to the coilover spring rate > stock spring rate, and the spring rate of the sway bar is unchanged.
Sway Bar Calculation info.
Calculation for solid bars
I contend that if you select a swaybar for otherwise stock suspension, you'll need a different/larger bar if you change the spring rate of the suspension springs.