Since I already talked extensively about the lobster, I will only point out the differences between the lobster and crab in anatomy, not repeat what I already said. The crab is wider and usually pictured walking sideways. Crabs are commonly in groups and use their muscles in their claws to battle other crabs for mates. Lobsters are more solitary creatures and prefer to live alone until they mate. As a result of the crab's smaller and sleeker size, it can hide in hard o reach places and evade predators easier than the lobster. The crab can use its powerful swimming legs to wedge itself between crevices and other places lobsters cannot go. Finally crabs are almost the waste management system for the ocean. They scavenge and collect trash at the bottom much more frequently than lobsters.
The image above is from http://home.earthlink.net/~wweinkle/Crablab.htm
The image above is from http://home.earthlink.net/~wweinkle/Crablab.htm