The charts below summarize some of the findings of a spring 2013 Pew Research survey of 37650 individuals in 39 countries.
Look first at the results from the Muslim majority countries. We see the largest divergence of views for the United States and China in Pakistan where China appears to be very favorably viewed, while the United States appears to be viewed rather differently. In general these countries seem to view China more favorably and less of a threat. However, most of these countries seem to prefer the American economic model and most give America more credit for respecting the freedoms of its own people.