Sports Science did this.
Sport Science: Run Or Slide? - ESPN Video - ESPN
They don't mention it in the video, but you can see when they overlay the runners that a perfectly timed head first dive gets you to the base faster although not by much, talking thousandths of a second. However, the risk associated with it and the room for error makes it pretty dumb to go head first. You should only dive if the first baseman leaves the bag and is attempting a tag.