China is much more diverse than you're giving it credit for, but for most of the past thousand years, China has been ruled by a single state, whereas Europe has been divided into dozens of national states since the Middle Ages. This can partially be attributed to the principle that land divides and water joins; China is crisscrossed by canals, lakes, and navigable rivers, which facilitate travel and trade throughout the country. I'll admit that this is just a supposition on my part, but to me, it makes sense that use of logographic characters, instead of phonetic characters like one sees with the European Latin alphabet, facilitates a shared literary culture, especially when that culture has thousands of years of state support to draw on.

Furthermore, I'd submit that there is a common European cultural identity, even if it's not necessarily the foremost identity. There's the Roman Catholic Church, the institution really at the heart of the West, and most educated Europeans have heard of the same great philosophers -Aristotle, Plato, Descartes, Kant-, draw on diverse classical musicians, like Austrians, Germans, French, Italians, and Russians, and share certain political terminology; the dominant unit of European politics is the state, which governs a territory without interference from neighboring states, and most can tell you what a constitution is, or an absolute monarchy, or democracy or a republic. There is have a common understanding of major religious, cultural, and political norms, so its hard to say Europe is dramatically fragmented compared to other regions.

About India it only appears unified on the map. Up until British dominance the subcontinent was divided into many small kingdoms and counties, and even the Brits had to walk a very careful line of dividing their territories up by ethnic groupings and they still had to pay respect to the existing divisions of India when they started taking it over (look up the Princely States).

Even after independence from Britain India couldn't hold together. Pakistan had to be created to avoid a political catastrophe, and its eastern part then broke off to form Bangladesh. Ethnic conflicts were and are still a common problem on the subcontinent, not to mention religious ones. That India even survived as a unified federation with fairly autonomous states was itself almost a small miracle. It's an incredibly diverse area with many cultures, religions and ethnicities all clashing together in a relatively small area.

So India is not very unified at all, beyond perhaps the political aspect of the union.

Isn't this a very Western-centric view? Do China & India see themselves as one culture?