In many articles dealing with abdominal muscle development many of the exercises are being executed with or on a large ball often called a physioball, Swiss ball or balance ball. When using such balls however, you should keep in mind that many muscles contract isometrically merely to maintain your balance.
Because of this, and to remain in balance during the execution, most exercises are done through a short range of motion. Full range exercises on the ball can be dangerous because you would fall off at the end of the range of motion. Because of this you must be able to keep yourself in support and well balanced during execution.
Even when you can maintain balance some of the exercises can still be dangerous. For example, in the supine physioball trunk rotation you are told to lie face up on the ball with your lower and mid back supported on the ball. You are to hold a weight in your hands, usually with the arms extended out straight.
You then rotate slowly to the left and right carrying the weight toward the floor while rotating the entire torso. If done in this manner the entire upper body would rotate up to 90 degrees to the right and left. If you did this however, you would most likely roll off the ball and probably injury yourself.
To alleviate this problem most participants move the arms full range but not the shoulders. This defeats the purpose of the exercise and it no longer a good abdominal exercise. In fact, the benefits of such exercises cannot even come close to matching the development that can be attained from doing the reverse trunk twist and especially the Russian twist.
Doing exercises on a large ball may be fine for a change in routines or for beginners. But the benefits of such exercises are far from what can be achieved in some conventional exercises. Because of this you should not strive to be trendy but work to get the development that you need and desire with some time-tested and proven exercises.
See Biomechanics and Kinesiology of Exercise for more information on the reverse trunk twist and other abdominal exercises.