This question is asked very often due to the big difference in price between the 2 options.
An aluminum housing is normally 3D modeled and designed to a specific camera. Due to the fact that basically any shape and design can be CNC machined from this material , the housings are usually smaller , more contoured to the camera and more ergonomic. Having a housing body that is camera specific allows positioning the buttons in accurate locations and shaping the housing to a perfect grip.
In addition , Aluminum housings do not get warm in the sun thus don’t require any silica gel or other moisture absorbent to prevent the lens from steaming up.
Polycarbonate housings are usually molded in a universal size that fits more than one camera and then drilled to allow the camera specific buttons. This usually results in a larger , less ergonomic housing.
Aluminum housings are considered more reliable as the material will remain as good as new even after many years and thousands of dives, this is not to say that Polycarbonate ones are not reliable, just that in the long run Aluminum is probably better.
Aluminum housings will also allow you to go deeper and support advanced flood-proof technology such as a vacuum system, available on Nauticam & Aquatica housings.
* Update – The Vacuum system is now offered on polycarbonate housings by Fantasea, Ikelite and Nimar as well.