Brown sugar is basically cane sugar + some molasses. If you're goal is really to get the molasses into your beer, I suggest adding that directly instead of having to add gobs of cane sugar along with just a little bit of molasses.
Dunno what the difference is exactly, but I wouldn't imagine it'd be much, other than the fact that your LHBS probably charges twice as much. I've used generic brown sugar from my local grocery store and have had great results.