I tried both a helmet mounted action camera and a handlebar mounted action camera. Neither produced images that were worthwhile. The depth of field and perspective were all wrong so scenes that I thought looked good and worthwhile of a photo looked awful once on the computer. The additional weight and bulkiness as well as awkward social interactions were a turn off as well.
Stopping to take pics with my iPhone is much better. Although I've become quite adept at sliding it out of my framebag and taking photos on the go as well. There are some things I miss that I would like to have photos of - namely wild animals I cross paths with - but there's no way I'd get those unless running a production quality cam the entire ride anyway.