Copper/brass cores would be more efficient if the cores where made the same dimensions.

The alluminium cores are usually made with thicker tubes(more tube to fin contact for a given core depth) This is where the increase in efficiency is over the copper/brass core. The copper/brass cores cant be made this way because the thin walled tube cant handle the pressure, and over time the tubes try to become more round swelling the core. You sometimes see copper/brass radiators that are bulging at the sides, often pushing the steel straps off. This bulging also often pulls the end tubes out of the header plates(very hard to fix).

The alluminium core doesnt have this problem because the tube side walls are thicker and because of the brazing used to hold it all together.

The ally cores are less likly to be holed from stones etc. but if they do get holed they are nearly impossable to repair.
Stray current corrosion can also be a huge problem. Usually only on cars with a lot of extra electricals(EFI etc), but can be solved with good earths/groundings.

The advantage of copper/brass radiators is they can be easily repaired or cleaned out. larger cores are often available(extra row of tubes) if cooling is an issue.

Thermo fans only work at low speeds and actualy hurt the cooling performance once the car is over about 60KMH.