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By most measures, China and Russia are two world powers headed in opposite directions in terms of their role on the world stage. China has emerged as nothing short of a geopolitical juggernaut, sporting a booming economy and a surging population, with a steadily growing military profile to boot. Meanwhile, Russia remains more or less adrift in the post-Cold War world. Talk of its future has been dominated not by lofty geopolitical aspirations, but rather by concerns about a shrinking population and the fate of an economy staked largely to finite oil and gas reserves. (Energy products and raw materials account for more than three-quarters of all Russian exports.)

The fade of one superpower and the rise of another may seem like a recipe for conflict down the road,...