Well, if they were both mutable or both immutable, why would we need two classes?
Immutability is a good thing for value holders (like String, Integer, etc.--Date should be immutable too, IMHO). It means you don't have to copy the thing for fear of someone else modifying it, keeps code simpler and lets it more directly express your intent.
Mutablity is a good thing for when you need to build up a value to put into an immutable value holder, or for when things do legitimately need to change and you don't want to have to create whole new object.
Why do both screws and nails exist?