A recent study indicates that those looking to maximize the effectiveness of their core workouts should look to the stability ball.
According to the Journal of Strength and Conditioning Research * untrained women who used a stability ball in a 5-week exercise program achieved greater gains in torso balance and electromyography (EMG) activity than women who performed traditional floor exercises without the ball.
In layman's terms this means that more muscle fibers are recruited for stability ball exercises than when the same exercises are performed on the floor. The result is a more efficient muscle contraction that uses more muscle fibers and improves muscle memory. This means that over time muscles not only grow stronger, they're also better able to perform the same tasks in the future because they have adapted to the stimuli received. Proper execution of stability ball exercises is critical to achieving these results.
*"Time to Get on the Ball," IDEA Personal Trainer Periodical, February 2004, pg 8. (references: Journal of Strength and Conditioning Research (vol. 17, pp 721-5).