China is interesting because you can really use it both ways: Free market enthusiasts will argue that China took off after it embraced free market reforms. State intervention enthusiasts will argue that China has been so successful because it is still very far away from the "free market policies" which e.g. the IMF is pushing on poor countries. In particular it has totally not opened up its capital markets or many of its import markets.
And the same holds for the ex-Soviet economies, too: The ex-Soviet economies that have done best are those that have joined the European Union, which most people especially on the American right would not exactly call a free market paradise.
For me, the answer to this apparent contradiction is actually quite simple: as so often, the answer lies in the middle. Total deregulation and extremely opening up your markets probably is not a good strategy to quickly pull your country out of poverty. But too much state intervention is at least as big a recipe for disaster.
Also, I would add that the optimal level of state intervention probably also depends a lot on how corruption-free your government is: with a very well functioning, corrution-free bureaucracy, you can operate effectively at a higher level of state interventionism (e.g. Scandinavia, Singapore) than if you hand that power to corrupt and/or inept officials.