Both thermal conductivity and emissivity of Cu are higher. The emissivity, which is a measure of how the material transfers heat from the surface, may be even more important then the Thermal conductivity. So Cu has great properties, but as I said above there is more to problem then simply material properties. If the question was that easy then there would be no discussion. Clearly there is much discussion over this topic, put nowhere will you find a definite answer. That is the point I have been trying to bring home to you.
2 things bite you, the expense of Cu and its poor machine-ability as well as difficulties casting it. Unfortunately as I mentioned above, CU is not as machinable as AL. (Do I have to show the chips I have made in the past to prove my knowledge!) Having attempted to machine Cu and having machined and cast lots of AL, I do have some experience at this level. While Cu is castable, the temps required are much higher thus requiring more capable furnaces and perhaps an inert atmosphere. Al is very easy to cast, it has a low melting point and wonderful fluid properties, this is why you see some many Al products.
The amount of energy required to cool a CPU are still low enough that completely adequate heat sinks can easily and cheaply be made from AL, the extra cost involved in Cu, both material and fabrication, to not result is sufficient improved performance to be warranted.
One thing you need to learn in life, often, the more eager someone is to claim absolute knowledge, the more likely it is, that they have no clue what they are talking about.