The article that you linked to, has one drawback that you seem to have missed: it used the exact same dimensions, for both the Aluminium and the copper heatsinks that are tested.
If you understand how significant that is, then you understand that because of the different natures of the material, the design needs to be different, and that comparing the same exact dimensions in both materials is flawed.
Let me give you a follow up scenario: take the same heatsink, and lower the base thickness to 2 mm. what you'll find is that the Aluminium heatsink performs worse, because it's unable to dissipate the heat which is now too concentrated, and the copper might perform a little better, because it is more than capable of handling the concentration.
That's theoretical, and not fact, but that's the essence of what I'm trying to relay.
The author probably took an off-the-shelf Aluminium heatsink that was optimized: it was specifically designed to run at the highest level of performance that Aluminium can give, under the expected conditions. If you took a design that was optimized for copper, and reproduced it in Aluminium, the difference would be huge.
Typically, copper HS will have thinner fins, and a thinner baseplate than Aluminium. The Aluminium counterpart of the copper-optimized design would perform dismally.
If you caught any of the above, then I'd like to get into a discussion of the fin-to-gap ratio, for different fluids
