Aside from its obvious sweetness, sugar does many other things when it comes to recipes. For instance it’s the basic building block of any dough, because it establishes the overall pH. Also, when sugar molecules meet water molecules, they form a strong bond. This bond of sugar and water affect the texture of cookies. Those are the main functions sugar has in a recipe. But now lets look at Brown sugar and White sugar, and see how they make a slight difference in a recipe depending on which one they use.
White sugar is made from sugar cane and is refined to get rid of impurities. Aside from brown sugar, white sugar also helps keep cookies and other baked goods moist and soft. However, the most important thing white sugar does for cookies is it creates tenderness. Baked goods such as cookies get their shape and structure from proteins and starches, which firm up during baking and transform soft dough into well-formed cookies. But because they build structure, proteins and starches can potentially make cookies tough, too. So like I said above sugar in cookie dough takes water away from proteins and starches, which help control the amount of structure building they can do; resulting in a tender cookie.
Brown sugar compared to white sugar is only partially refined, meaning it still has some molasses clinging to it. When you bake with brown sugar you will notice that it adds moister to the recipe and that’s because of the molasses content. Now because of this you might need to adjust some of the proportions in your recipe, like slightly decreasing the wet ingredients or increasing the dry ones. I have said this before in other post but I will say it again because it’s very important to remember that baking is all about balance, and with brown sugar included in a recipe you need to balance out the moisture it offers to the recipe.