I'm going to agree with the helmet or chest mount. Even on fairly smooth pavement, the handlebars are vibrating more than most cameras can compensate for, and you have to turn the bike to capture the view to either side, which isn't always convenient.

I'm modifying a spare helmet for just this purpose, and for the exact reasons you've seen, here. The video is very hard to watch when it's shaking and bouncing like it did on the handlebars.