Power
You wouldn't be as powerful as, say, the military dictator of a small island nation. That's a good thing, though. As a choreographer, you'd probably get in a little legal trouble if dancers who defied your will began to mysteriously disappear. You may, however, be able to rule your rehearsal room with an iron fist.
Of course, the choreographer is not always the only one with her hands on the steering wheel. For example, if you're the choreographer for a Broadway musical, you have to answer to the director. There will also be a gaggle of other creative types inserting their opinions—composers, playwrights, diva stars. While you'll have control over the dancing, you'll have to find a way to make your vision jive with the visions of all the other busybodies around.