It depends on many variables.
How portable do you want it? Thicker = heavier. Yes, this means you can so over-build an aluminum case that it out weighs an off-the-shelf steel case.
What is your budget? Thicker costs more.
How do you plan to work on the material? Thicker might be better for methods such as drilling, tapping and beveling. Thinner might be better for bending. So, what tools do you plan to use? Bending brake? Drill press? Router?
Note that you can (and probably should) use different thicknesses for different parts of the case. For instance if side panels are not load bearing, feel free to use thinner materials than the rest of the pieces. Just don't go too thin, because aluminum can get too flimsy.
For steel, I've seen as thin as 0.5mm and as thick as 1.0mm (those old Chieftec server cases come to mind). Typical good quality cases are 0.8mm thick.
For aluminum I think 0.8mm is around the thinnest, and I've seen as thick as 2.0mm for higher end cases (Trivia: BFG Phobos case used 3.0mm for the shell).
When you buy raw case materials, you may see them sold in "gauge" similar to how wire is measured. For instance I've purchased "plate aluminum" that was "0.63." Plate is thicker stuff. Great for drilling and tapping, but you probably won't want to try bending it even with a bending brake.