It is difficult to tell the exact differences between them,as it all depends on the context. Personally, I would think the meaning of 别 is sometimes slightly stronger, for example, 别动! is much stronger than 不要动! In addition, when you use 不要, you normally use it with a verb, but you don't have to use a verb after 别. You can simply use 别 to refuse something or disagree, and again the meaning is rather strong. But on most occasions they are interchangable, and people from different regions have different preference. When both words could be used, I feel people from the south tend to use 不要 more frequently than people form the north. Hope this helps.