Plastic cases might actually be a bit better than steel depending on the radiation type. Neutron radiation is more effectively shielded by interacting with light atoms so stuff with lots of hydrogen atoms like water or polymers have a better chance of interacting with neutrons and slowing it down so that it can be stopped. Steel is probably better for gamma radiation or charged particles like muons.

But overall, pc cases are probably too thin to appreciably affect the radiation levels. Cosmic rays and their secondary radiation is fine with going through buildings so a 1mm thick case isn't going to do much.