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It all depends on what species you are looking at. For instance, I would say that a Moorish Idol is more likely to die and/or get sick than a hermit crab, but I would also say that a shrimp is probably more likely to die and/or get sick than a Damsel.
Also, remember that invertebrates like Shrimp are sensitive to poor water parameters, whereas some fish (like Damsels) have a better chance of surviving in a tank with poor water quality.
Yes certain shrimp and many crabs are very hardy. Remember many of the crabs and hermits can be found in the shores which are regarded to many of us as the seas protein skimmer.