Copper is superior in thermal conductivity, by a large margin. Aluminum is a good thermal conductor, but it's not in the same class as copper.
That said, most people water cooling a computer are only looking to get rid of a hundred watts or so. A nicely designed Aluminum radiator is more than adaquate for this task.
The only remaining issue is the kamakozi interaction between Aluminum and other metals. If you use tap water, the Aluminum core will develop a leak sooner or later if you have a copper block. If you use distilled and keep the liquid non-conductive (water wetter, occasional water changes changes, etc.), the core can easily out-live your computer. If you get paranoid, you can get a magnesium anode from your cooler supply store for under $10, just pay attention to how it's grounded.
If you run a TEC, I would HIGHLY recomend a copper core. But for regular PC wattage, it's just a matter of convienience. Just pay attention to what liquid goes into your PC, and you'll be fine.
Again, regarding thermal properties, Copper has Aluminum beat hands down in EVERY respect. But getting rid of a hundred watts or so is easily done in either Aluminum or Copper. Surface area and CFM play a much more inportant role than what the core is made of at these low tempature differentials (ambient vs. water temp).