Cinnamon Roll Filling
What I learned researching this question:

Brown sugar has anywhere from 3.5 - 6.5% molasses depending on whether it is light or dark brown sugar. Molasses is what makes brown sugar brown.  Brown sugar has a smaller granule than white sugar.

What all this means to a cinnamon roll filling:

When brown sugar and cinnamon (and butter) are used in the filling, the brown sugar becomes more liquidy and less gritty than white sugar.  The flavor is richer and more complex.  When I make rugalach or almond rolls, I prefer white sugar, cinnamon and butter for the filling which lets the almonds or walnuts bring the flavor to the pastry.  Cinnamon rolls do not usually have nuts so the pastry requires more flavor from the filling ingredients (and the icing, of course!) 

Here's the site where I read about brown sugar:

http://en.m.wikipedia.org/wiki/Brown_sugar