To me, most of the time, "Would you..." and "Could you..." are equally polite if we don't split hairs.
If you ask a teacher to help you with a problem, "Would you..." may be more appropriate. "Could you..." may sound like something associated with his/her ability of solving the problem. On other occasion, "Would you..." may sound like an order.
So it depends on many factors, such as your tone of voice, the mindset of the listener, etc.