This is taken from the Emirates conditions of carriage:
9.3 Denied boarding
9.3.1 If we cannot carry you in your ticketed class of service on a flight for which you have a confirmed reservation and have met all applicable check-in and boarding deadlines:
9.3.1(a) we will carry you on one of our later flights in your ticketed class of service or, if you choose, we will carry you on another of our flights in a different class of service. In the event of a downgrade from your ticketed class of service we will refund you the difference between the applicable fare, taxes, fees, charges and surcharges paid for your ticketed class of service and the fare, taxes, fees, charges and surcharges applicable to the class of service in which you are actually carried.
So it would seem you are entitled to a partial refund.