Brown sugar is just the same as white sugar, with some molasses left over from the refining process, so there should be no difference in nutritional value.

It does not matter. Brown sugar has other stuff in it (that said, it's a grass, and while we eat grasses for energy, we don't eat them for nutrients) I believe this means that brown sugar also has (by weight) a higher caloric content, i.e. it contains more fuel. Of course, that just means that you have to eat more of the other kinds of sugar to equal a given amount of brown sugar, so really it doesn't matter.