It is not a "free market" system.
You are going to have to flesh this out a bit more. What time periods are you talking about for each? Be more specific.
China was under a centrally planned socialist model... key words: centrally planned... until the 90's. As late as the 90's... they could barely feed their own people. It has been the move toward a more free market/capitalistic economy that has made them the #2 economy in the world. As we move in the wrong direction... they will soon over take us by moving in the right direction.
Keynesian is absolutely a market economic system.
China does not follow Friedman policy in any way, shape, or form. The economy is still centrally planned BUT replacing production quotas with market signals and information. The market can be very good at relaying information (and it can be utterly defeated as well, but, when working properly, this is its great strength).
There is no doubt China has adopted some of the neo-liberal agenda. However, it is more telling what is HAS NOT adopted that has made it the #2 economy in the world. It is interesting to reflect on why the Western World still refuses to adopt the full neo-liberal agenda itself, and why, those countries that did, have had such wrenching and bloody experiences, as they get back to Third Way, pragmatic policies.
There are many lessons to learn as we look at this End Game of Capitalism. We have this serious imbalance between the totalitarian visions of the Left and Right.
Third Way, baby. But we are inside a Crisis of Capitalism that requires retooling the whole game.
China was still feeding its own people even during the worst of Mao's experiments. In fact, it is only now that China has become a grain importer, I believe.