Some scholars of international relations do argue that the bipolar world of the Cold War was more stable because the two superpowers dominated the world and could prevent any serious wars from arising either between themselves or between client countries. This limited the potential for instability.
However, it is easy to find holes in this theory. The world of the Cold War was not noticeably more stable. There were superpower conflicts such as the Cuban Missile Crisis which were much more dangerous than anything since. There were larger scale wars (Vietnam, Afghanistan, Iran-Iraq) than there have been since. These conflicts (and the fact that similarly dangerous conflicts have not arisen since the end of the Cold War) suggest that the supposed stability of that era was not all that some scholars make it out to be.
For these reasons, I would argue that the post-Cold War, post-bipolar world is no less stable than the Cold War world was.