A high-quality fleshing knife should be extremely sharp. The sharp side must be razor-sharp for maximum efficiency. Its main role is to shave the gristle off animals. On the other hand, the other size is supposed to be dull. It is most commonly used to push the fat.
You may find a fleshing knife with two edges though – while they are quite versatile and useful, this is not always a general rule. Other than that, not all manufacturers sharpen their fleshing knives, so you might need to do it yourself once you receive the tool.