lol because everyone wants to be Mr. Universe.
The idea that lifting heavy weights is only for bodybuilders is absurdly wrong. Weight training is immensely useful whether you are trying to be a better runner, get stronger, lose weight, or develop your "core". There are few things that can replace the effects of lifting heavy stuff and people who avoid it typically have a very poor understanding of human physiology and exercise in general.
The real comparison here is whether or not an individual doing crunches (or whatever exercise) on a swiss ball is getting a better workout than the same individual doing the same exercise NOT on a swiss ball.
No, the question is whether doing training on a stability ball (or any similar device) is the best way to develop your core. In the vast majority of cases, it isn't. Limiting the argument to "exercise X vs. exercise X on a stability ball" just doesn't make sense when some exercise Y is a much better choice for strengthening your core. In particular, squats, deadlifts, presses, etc will increase the strength of your core MUCH more effectively than either crunches or crunches on a stability ball. For that matter, the barbell exercises will strengthen your core far more than just about any of the exercises on a stability ball. And before someone asks, doing barbell exercises on a stability ball is (a) more dangerous and (b) ultimately less effective than doing them as intended on the floor. I started to write an explanation of why, but the Rippetoe article I linked earlier explains all of this far better than I could. If you haven't already, I highly recommend you read it.