Crayfish are quite different from shrimp. For one, the dwarf shrimp the OP is speaking of get to a little over an inch long. Crayfish can get over 5" long. What does this mean? It means that shrimp have more predators, basically anything in the tank other than small mouthed or young fish. How many predators would a 5" crayfish have in the tank?
Crayfish are also predators by nature and they have larger front claws to kill fish. They are considered to be mildly aggressive and have little to fear. Nearly all shrimp are detritus feeders, scavengers, algae eaters, or a combination of all of those. They are considered to be timid for the most part, generally not coming out unless sufficient groups are present. Crayfish do fine all by themselves. So as you can easily see from these general comparisons, they are not that closely related.