This picture perfectly sums up anything I could say about why you need a good headshot. Look at the two, and ask yourself the following four questions:
Which picture is more professional?
Which is more likely to land an assignment and get paid more money for it?
Which one will have editors calling him with assignments?
Which photo do you want to be?
In a perfect world, you'd be judged solely on your writing ability. The world, unfortunately, is not perfect. In fact, even if it were, your picture would still come in to play.
When choosing between two writers of equal skill, an editor has to make decisions based on perceived intangible qualities, such as punctuality, dependability, and professionalism. One of these photos effectively communicates all of those qualities.
In a world where your picture can mean the difference between a paying assignment and a rejection, why would you put anything but your best foot forward?