the last time the west only managed to "win" the moon race because it was competing against financially poor and poorly managed soviet state(all key brains behind soviet space program were released from gulag just to work on it and knew that if they will not please their masters they will go back to gulag and die. the greatest motivation of all time)

china now is a lot more sane people that don't mess with politics/publicity enjoy comparable levels of freedoms to the west(In a lot of cases more economic freedom but in all cases no political freedoms) which makes them much more likely to succeed competing against corrupt west as it is now