This question is almost unanswerable.... what do you mean by Balance of Power? History is not some kind of scale with clear periods of chaos and balance, different eras in different eras had different economic, political, and social constructs. If you want a point in time when the world was dominated by two superpowers then the Cold War or Roman/Han times would probably be the best bet. If you are looking for the largest balanced empire then the Mongolian was at one time the largest.... but like I said before this question is really terrible.