Yeah, cultural, political, social, there are a lot fo factors that affect economic outcomes. Ironically, it may well be India's tendency towards socialist command-economy, privilleged special-interest economics (subsidies), etc that is holding it back.

The lack of a need for an electoral mandate has freed the Chinese government from the need to actualy implement socialist policies (or on fact any particular policies, they can do what they like, regardless of what the people think about it using their communism 'with chinese characteristics' get-out clause).