Hi Ming, that's a great question and perhaps one for a future Cameralabs group test...
70-300 IS pros: Affordable, relatively small and light, IS, range
70-300 IS cons: basic build quality, rotating front element, slow focusing
70-200 L pros: better optical and build quality. Better weather-proofing. Quicker and quieter focusing. f4 aperture throughout range
70-200 L cons: no IS on old model. Not very discreet white barrel. Heavier. Not as long a range.
Having used both, the 70-200L is clearly a far superior lens, and if you;re shooting candid street photography, you'll love its faster focusing. BUT people will stare at your white barrel!
As for IS, it sure is useful, and you'll no doubt know Canon recently released a version of the 70-200 f4L with IS, but it's much more expensive. As it is, it makes the 70-200 non-IS look like a bargain.
I think you really need to visit a camera store and try them in person though. I reckon you won't miss the extra 100mm, and will be seduced by the superior build, quality and focusing of the 70-200 f4L.
If you're in a store, try out the 70-300 DO IS as well. It has the 70-300 range, IS, and quick, quiet focusing, along with a smaller, more discreet body, but the quality isn't as good as the 70-200 L, it's pricey and it has a strange bokeh due to the DO element. It is a neat lens though.