Copper is good at absorbing and conducting heat but not so good at radiating that heat away into another body.
A very small portion of the heat dissipated for our purposes is removed via radiation. Most heat would be removed by conduction and convection, and the difference between aluminum and copper should be minimal also in regards to cooling from radiation.
There are a lot of theories and stuff about aluminum and copper mixed, and why they use it in commercial coolers.
Aluminum is lighter, cheaper, and stronger in some alloys/forms hence why it gets used. In some situations, the differerence could be only academic. (Where thermal conductivity of the metal isnt an issue, and surface of the heatsink is the determining factor of the steady state temperature)
When pure thermal performance isnt the sole design factor, and cost, weight, strength, ease of manufacturing, durability, start coming into play, thats where aluminum takes the lead. You see copper slugs set into aluminum heatsinks because at the source of the heat, where there is a high temperature gradiant, and high "thermal density" (unsure of the actual term... Watts per mm^2) the advantage of the copper is significant. Once the highly conductive copper spreads it out, and you just need bulk surface area to get rid of the head, aluminum is the most cost effective option.
Now, lets see some of the CPF manufacturers start friction welding some copper heatsinks into an aluminum body for the best thermal transfer across the parts ;)