I have heard Doug Casey explicitly make this claim, and other free marketers say similar. I was surprised to see that Heritage.org lists the U.S. as having significantly greater "business freedom" than China. A comparison is here:
http://www.heritage.org/index/visualize?countries=china%7cunitedstates&src=ranking
"Business freedom" includes government regulations, so the mainstream narrative would be that China is more deregulated than the U.S. therefore offering an advantage in that input.
Does Hong Kong count?
I do not have first-hands experience, but some events are disturbing: http://www.economist.com/node/21543593?fsrc=scn/fb/wl/ar/whogoestothegallows.
sentenced to death in 2009 for illegally raising $120m in funds from illicit sources (ie, not official banks)
Being sentenced to death for raising capital does not sound like business freedom.
As far as I can tell it's a definite crap shoot. China has infinitely more regulation than the United States does, but the U.S does an infinitely better job at enforcing the regulations that it has. Therefore it may well be easier to start a small business in China, but you'd better watch out, because there's very little legal protection and you could also have everything confiscated from you and thrown into jail. On a somewhat related side note I bet that by an large small businesses have higher profit margins in China (depending upon what their tax code is like, something that I am ignorant of), because it's had a lot less time of industrialization and of capitalistic enterprise, both of which would mean that there are probably fewer competitors on local markets, both of which help to justify the risk.
For non multi millinonaire's who live in the US and have no connections in China - I would bet for most people it would be easier to open a business in the US
"As in a kaleidoscope, the constellation of forces operating in the system as a whole is ever changing." - Ludwig Lachmann
"When A Man Dies A World Goes Out of Existence" - GLS Shackle
As a foreign business, it would be very difficult. You would need to partner with a chinese firm first for best success.