There are many differences between training on a stability ball versus a traditional bench. The most obvious difference is that the ball provides an unstable surface and therefore increases the level of difficulty of the exercise being performed. When performing the seated Bicep curl for example, when sitting on a bench you can focus all of your energy and attention on the arm exercise. But when you are sitting on the ball, you must first balance yourself and continue to keep your core engaged as you perform the bicep exercise.
At the same time, another advantage of using the ball is that more muscles are involved making for a more complete workout. This allows for a more efficient workout in that more muscles are engaged at all times during your stability ball work compared to working on a hard/flat surface.
By engaging more muscles, you are also burning more calories. Incorporating more stability ball work will force more effort involved to complete the same amount of exercise which will have a positive effect on your metabolism. Substituting the stability ball with your office chair is another trend growing in popularity that accomplishes this will help to burn more calories at rest.