MUMBAI—Shaped by disparate political, economic, and social forces, and starkly divergent histories, China and India, though neighbors, have arrived at a point where their young people, as well as their leaders, have developed individual paths toward each other and the world. For a host of reasons, the two nations remain at odds 30 years after both economies and societies truly opened to global markets and outside influences.

Take the attitude toward house ownership. Indians love to invest in their homes, decorating them with works of art, exquisite furniture, and high-tech gadgets. In India, the home is an extension of the self. Family and professional colleagues are routinely welcomed into both rich and poor households. In contrast, a Chinese may own several homes, but these remain zealously guarded private domains, functional in nature and primarily used as a place to sleep at...

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