Have you taken a good look at your tires?
There are roughly 3 things to look at when looking at sway bars (or anti-roll bars).
1. Do I have too much oversteer? Meaning steering is very responsive and rear end sometimes breaks loose while the front end is stable.
2. Do I have too much understeer? Meaning car has tendency to drift or push through turns. So you try to take a turn but the car wants to keep going in the direction that it was going. In this case, your front end has broken loose, but the rear is planted.
3. Chassis roll. You hit a turn and the whole car leans and you feel like you are about to fall out of your seat.
Everything that I am about to say is assuming that you have good tires, and shocks/springs are in good working order.
For #1, you would want to move up to a larger front sway bar. This will actually cause you to loose a little steering (only noticeable when cornering), but it will change the overall balance of the car such that the rear end shouldn't break loose.
For #2, you would want a larger rear sway bar. This will actually cause you to gain a little steering.
For #3, the bigger the better. The bigger the bar, the less the chassis will roll. However you can also adjust this with how stiff your springs are and the amount of dampening in your shocks.
The thickness of the bar basically tells you how well it will do its job. However you have to pick the appropriate sized bar for your application because it is all about balance. For example, if you were running the 3-legged race, you wouldn't pair Carl Lewis up with a 5-year old. Yeah, Carl is fast, but the end result isn't gonna be pretty. You have to get the right sizes to get the desired results.
Another way to remember how to pick the bar is if you have traction problems on one end of the car, you put the bar on the opposite end. Not enough traction up front, put the bar in the rear, and vice versa.
Also remember that it is generally safer to have understeer as opposed to oversteer. Reason being if the front end doesn't want to turn, you can usually just hit the brakes, slow down and you are ok. However if you have oversteer, there isn't much that you can do once the rear end starts to break loose, unless you are a good driver.