That's actually an interestin­g point; I don't think either of them will make achieving that sort of global hegemony a goal of their foreign policies.

China, by its traditions­, is more immediatel­y concerned with ancient territoria­l claims--I believe that they would be quite satisfied with keeping Tibet, Inner-Mong­olia, and the Uighur regions under their control, than trying to act as global cops. Their only expansioni­st desires would lay in the direction of Taiwan, and possibly Korea.

India I don't know as much about. What I do know is that it is a very structural­ly challenged nation--th­ey have hundreds of different dialects, and dozens upon dozens of different cultures within their borders. They already constitute an empire, of sorts, and I don't think it's likely that they will harbor any superpower ambitions beyond developing what they already have. Pakistan and Bangladesh­, and possibly Sri Lanka would be the only candidates for expansion I would see, but since the Pakistanis have nukes and India is on good terms with those other countries, that doesn't seem very likely either.

To further make the case against India and China trying to claim the vacant mantle of 'superpowe­r', I really think that the ability to amass the sort of relative advantages necessary in economic and military terms to achieve that sort of dominance in the world has disappeare­d, and probably for good. The United States was the first, and probably the last superpower­.