Dampers (shocks) don't change much about the balance on the car, that's all in the springs. Going too stiff on your dampers will result in less control of your car because the springs won't be able to do their job, resulting in loss of tire contact patch force.
The job of dampers in a car is to control wheel motion that comes from resonance in the springs. Springs are what control body roll and ultimately the balance of the car.
Sway bars also control body roll, but because of the realities of cars, sway bar motion is generally less damped than the springs, so it's desirable to control your body motion with springs and use sways bars as a final tuning tool.
At the end of the day, you can put a set of decent lowering springs on your car with a set of KYB Excel G dampers and learn a lot about your car. I had no trouble keeping up with Miatas and Caymans in my MR2 with a set of Eibachs and Excel G's (and good tires). Good tires are what really change a car into a track car. I've got Falken RE615K+'s on my MR2, although I've heard Direzza Star Spec II or RE71R are better tires and have more grip.