The cable chop sounds great on paper, but when it comes to the execution it's less of a core exercise and more of an arm blaster. Also, the resistance changes drastically from beginning to end.
With this method, the Swiss ball acts as a cam similar to what you'd find on a machine, giving you the feel of constant, equal tension throughout the ROM and putting that tension right where you need it.
Although this article is aimed at athletes, if you're looking to get into shredded, athletic shape, try some of the exercises Coach DeFranco describes. You can practically feel the fat melting off your body!