Not nearly as much. One single picture is open to each person's individual interpretation, hence the one thousand words. A video is a series of pictures that has been given a meaning by dialog and the pictures before and after.
Some of the videos I've seen? Not a hell of a lot.
Of course, it all depends on the circumstances. While the phrase is largely cliched, a picture or a video can be invaluable in a court of law. It's hard to argue with the evidence of your eyes (Photoshop notwithstanding).