China and India are both large, highly populous asian countries that the European colonial powers tried to get their hooks into. This may not be accurate, but I get the impression that now that both countries are free from direct interference in their affairs, Indian culture has been much more affected by the process than Chinese culture has.
I'm talking about things like the Indian government seeming to be based on a British system and using English for many official purposes, while in China, the entire government structure seems to be home-grown, and English has no official status outside of places like Hong Kong. I think that, during the British Raj, armies of Indian troops were formed and fought for British interests, while I haven't heard of any foreign nation forming armies of Chinese troops to use for their own purposes.
Is this impression accurate, and if so, what are the reasons behind it? Did the nations/areas have different levels of national unity prior to colonialism? Did differences in how they were administered as colonies have an effect, or how the process of freeing themselves from colonial influence went?
The vast bulk of China was never formally colonized in the same manner as India. The British Raj maintained direct administrative control over large areas of India, and the remainder was ruled by tightly controlled puppet states. Britain exerted a direct control over the administration and legal system of India, so it is not unusual that they would leave a large legacy.
The "colonization" of China really wasn't colonization at all. Outside of several small enclaves (Tsingtao, Hong Kong, etc.), China remained under the nominal control of a domestic Chinese regime. The colonial powers exerted their influence indirectly through "concessions", which were basically privileges granted to foreigners by the Chinese government. (Very similar to the treatment of the latter Ottoman Empire.) As such, colonial powers never displaced or replaced Chinese rule and custom, and were not in a position to make fundamental changes to Chinese governance.
TL/DR - Direct colonization of India replaced indigenous structures, indirect colonization in China merely leached off of the extant society. India was reformed, China got a bad case of hurt pride.
India was under direct British rule, even if the British often used "native" intermediaries. India had British bureaucrats running the government, and elite Indians received British education and were influenced by British culture.
China, on the other hand, was never colonized by Europeans. There were a few small European-run enclaves, like Hong Kong and Macau, or foreign-run areas in cities like Shanghai. And the Chinese government was bullied by foreign powers for some time. But the different foreign powers basically agreed that China would be an open area, and no one country would control it. So China maintained its independence. The Chinese government, bureaucracy, school system, military, etc., was run by Chinese people. So the foreign influence wasn't very strong.