Answer by Paul Denlinger:
I have spent most of my working career in China, and don't have experience with India, so I will focus on China.
Chinese government is dominated by one political party, the Chinese Communist Party. Other parties exist, but their role is to only act as advisors to the CCP. Everything is under the party: the nation, the military, the financial system, the judiciary (there is no independent judiciary), the mass media and all local governments must serve the party. Middle and senior positions in all these organizations are open only to party members. There is no compromise about this issue and it is not open to discussion.
The role of the CCP is to serve the party leadership first, the 82M party members second, then everybody else third.
Because of this structure, the party has a very powerful hold on the lives of China's 1.3B citizens. It also makes the party's internal reform impossible.
Since there is no independent judiciary, Chinese government officials, who are party members, have no system of checks to reign in their own corruption. In order to avoid being caught for corruption by the party's own internal organs, junior officials bribe senior officials all the way up the ladder.
Also, since all financial institutions and land property are under the party's control, all economic growth is simply about transferring money from the party's one pocket to another. See my answer:
When a senior party official is caught and prosecuted for corruption, it most likely means that he has fallen out of political favor, not that he was corrupt. (Because all senior officials are corrupt; it's just a difference in degree.) Because the judiciary is under the party, trials are usually very carefully managed and short, so as to save the party major embarrassment.
The biggest difference I see with India is that India is a multi-party democracy and has an independent judiciary and independent media. While there is major corruption, it isn't built into the system as it is in China.
Put another way, if there was a major effort to root out corruption in China, the Chinese Communist Party's one party rule could no longer exist.