BEIJING—Earlier this month, President Xi Jinping and Premier Li Keqiang both delivered forceful instructions on how to reform China’s state-owned sector. Their messages directly contradicted one another.

On July 4, officials of the State Council, China’s cabinet, were read remarks by Mr. Xi calling for “stronger, better, bigger” state juggernauts, with a central role for the Communist Party in their management. Mr. Li’s prepared comments stressed the need to “slim down” state companies and to “follow market rules” in remaking...