Making the base plate out of copper offers a few advantages over aluminum with the main reason being that copper transfers heat faster than aluminum. However, copper retains heat longer. Aluminum does everything the opposite way. It transfers heat more slowly, but retains it for a much shorter period of time.
So the best design is to have a copper baseplate on the bottom of your aluminum heatsink to transfer the heat away from your CPU quickly. Then the aluminum transfers the heat a little more slowly from the copper to itself. Then, finally, the aluminum releases the heat to the air more quickly than the copper, thus forming the optimum heatsink system.