In all fairness, it would be more of a case of a Moveclip being able to do things that a graphic symbol cannot, since a Movieclip has so much more to offer. But asking from the graphic side, the only thing I can think of that a graphic can do that a movieclip cannot do is it can contain a timeline animation such that if you extend the graphic along a timeline, the animation will play for the frames it occupies (I think it ends when it ends though). A movieclip will just sit there if it has nothing to make it play.
I only found this out about a year ago, and I have found no real use for it, but someone doing cartoon animation might.
I just wanted to make sure I wasn't missing anything here ;-)