danny, look at the graphs towards the bottom, thermal resistance for copper is consistently better than aluminium, for 100% same design, copper will always win. period. no questions on this, its not because one releases heat/absorbs heat better, its only because of the CONDUCTIVITY (please understand this) which is extremely important in forced convection
one thing you failed to show in ur comparison is the velocity (and flow rate) of the air through the fins. thinner copper fins could cause more resistance compared to thicker, more spaced apart fins; reducing airflow through the fins. Also, the design isn't optimal, with coppers much higher conductivity, you'd want a thin/short fin or fat/tall fin.
this is not an apples to apples comparison, and thus you ahve showed nothing. the link i have given u have the same design, and copper being almost always better. they said yes its possible to make aluminium ehatsinks as good, when u optimise the airflow through fins, which is easy since its much easier to machine aluminium. but copper would be better if you optimise it then.
water has a higher specific heat compared to air, and i'm sure you know the meaning. this is why its a better coolant than air. it doesn't compensate anything, instead makes heat removal better.
concentrate on the thermal resistance graph. this is the graph that allows u to see a difference, i'm sure i dont need to explain thermal resistance to you. the results they found, speaks for themselves.
cathars block uses copper yes because it absorbs, conducts and thus conducts the heat to the water better than aluminium. water/air/liquid metal this will always be the case.