There is very little difference, they can be used pretty much interchangeably.
But the "able" ending on any word usually implies personality - meaning that you are often talking about a person or a personified place or object.
If for example a chair was unsociable, you'd be implying that the chair itself has some kind of personality (being alive).
Where as if you say that a chair was unsocial, you would probably be trying to say that the chairs shape or characteristics somehow made people using it unsociable.