Cockroaches have legs for crawling on walls and ceilings, but grasshoppers have legs for jumping. Some cockroaches have wings for flying, but most others don't. Grasshoppers have wings for making a sound, whether it's to attract a mate or to just be annoying. Grasshoppers have a body that is split into multiple segments (more than just one), while cockroaches have only like 2 body segments. Cockroaches have barbs on their legs for a sense of touch, while grasshoppers don't. The legs of a cockroach are very sensitive though. Cockroaches can survive a nuclear explosions because the rads don't affect them. But the heat from the nuclear blast will certainly kill a human, as well as a cockroach if exposed. Obviously, grasshoppers couldn't survive a nuclear explosion. The only down side to roaches surviving a nuclear explosion is them turning into radroaches, like in the Fallout game series from the game developing company, Bethesda Game Studios! If there were a nuclear explosion, then the roaches would mutate into human head sized roaches that can actually attack a human! (this is just a theory, not scientifically proven, lol)
I hope this helps you even a little bit, have a great day.