Dark brown sugar contains more moisture because it has invert sugar and granulated sugar does not have any at all, so the moisture burns off in the oven.
Invert sugar consist of glucose and fructose, two simple sugars. Invert sugar is especially hygroscopic, meaning that it pulls water from whenever it can be found, the best source being the air. And invert sugar keeps on drawing in moisture ever after the cookies have been baked, thus helping to keep them chewy as they cool. So when it comes to chew in cookies, regular granulated sugar with its lack of invert sugar, is simply no competition for brown sugar!!!