At first glance, they seem to mean the same thing, but I think they're different somehow. When we talk of "the best", we might be limited to within a particular period or era, e.g. "the best fighter of the decade" or " the best fighter of the era". But when we say "the greatest", it's for all seasons or generations, or better yet, for all times. For me, therefore, the latter is wider and more encompassing in scope.