How effective is their navy?
Well, it hasn't (yet) had an engagement against a modern adversary, so we don't know how it would perform. Then again, the American navy hasn't fired in anger against a peer competitor's navy for some 70 years.
Of course, it comes down to training, equipment, morale, etc. We simply don't know enough about the Chinese on these parameters. What we do know is that they are making leaps and bounds on both the quantity and quality of their navy. For example, their 052D's AESA radar is at least one generation ahead of the PESA on the Arleigh Burkes.
Their ships are generally well maintained, clean with no visible rust, which speaks to a good level of discipline and dedication. They have also been able to continuously put to sea a task force to patrol the Gulf of Aden, which provides valuable experience to their personnel.
China's anti-ship missile technology is by all accounts cutting edge. Their AsM inventory is both comprehensive and advanced, and when armed with these weapons, their ships do pack a lot of firepower.
In summary, we are all curious about how well the Chinese navy can fight, but not curious enough to find out.