Is it timing or shutter speed? If you are filming video at 60fps, that is much faster than the speed of still photo? Thus the still photo allows in more light and thus better quality image.
There is a very distinct difference between video and pic modes for sure. But as @blabel75 says - pics will allow far more light than the video. I typically shoot video at 25FPS, just for file size purposes and the videos seem to be fine unless I go into "digital zoom" and then they do start to fuzz out the more zoom that is used. Yet, that is to be really expected.