Mythbusters looked into the cockroach thing, with some interesting results(scroll down to “Cockroach survival”, about 1/3 down). Basically, they found that while cockroaches can indeed survive radiation at levels lethal to humans, other insects did better.
As for why, here’s a quick summary from Wikipedia, with more details in the source material:
Meanwhile, our cells are dividing all the time, particularly bone marrow and the immune system. So we’re f’ed.