I prefer brass, especially the "360" type. It is much easier to machine than aluminum. Both are sufficient electrical conductors for electrostatic shielding and neither are magnetic metals so they are poor for magnetic shielding. Brass, right now, because of the price of copper, is fairly expensive but the ease of machining far outweighs the price difference in lost time.
Depending on how you plan to finish the outside, you might select one over the other. If you want to paint the outside or anodize it, you could use the aluminum. If you want to nickel plate it, for the more traditional microphone look, you would use brass. Plating aluminum with nickel is difficult and requires extra chemical processing steps.