As someone who raises crickets for pet food, I can confidently tell you that you needn't kill crickets. Just give them a water dish and at least 10 will promptly drown themselves. They're either suicidal, or so painfully stupid that the only reason they haven't been wiped off the face of the planet is the incredible rate they reproduce at.

In a less facetious sense, I do believe that insect neurology is substantially different. Crustaceans have a nervous system web, which is why you have to cut crabs and lobsters in half to kill them rather than just stabbing them in the head.