I agree that the ideology would be important for switching the situations between India and China, but I believe that language is just as important as well.
The Chinese language was consistently written in characters, and the writing system is probably the only one in the world still in use that is not an alphabet. This also assisted with cultural assimilation, as invaders were required to learn the characters, which were also closely tied to Chinese culture, in order to create any records. On the other hand, Brahmi was the first Indian script, and although Sanskrit was the first widely spoken language, it eventually spilt into many over time, each with their own scripts, which in turn helped to create various entities.
Unless you're willing to create a POD in which the Indus Valley Civilization survives, allowing a logographic writing system to predominate, I think the best scenario would be to create one in which the Maurya lasts longer, and enforces a commonly spoken and written language, such as Sanskrit and Brahmi. This would help to consolidate the notion of a "united" India after the dynasty's fall, in which the written and spoken components would probably function similarly to that of Latin in Europe. The challenge would be to ensure that another unified dynasty would come to power and sets a precedent for others to follow, but I don't think it would be impossible. Meanwhile, you would have to ensure that at least one of the northern nomadic groups that invaded China during 300-500 adopts an alphabet, possibly taken from states further west, because they realize that writing is important for maintaining a separate identity.