I’m not so sure. The PLAN is not very good in the feilds of logistic support, technology and training. It has 1 aircraft carrier, 15 destroyers, 50 figates, 50 SSKs, 9 SSNs and no SSBNs. The DOD estimates that 5 Type 094 are under construction.
I think Taiwan and Japan have stronger navies than China.
First of all, Taiwan does not have a stronger navy than China. Not even close. The current Taiwanese navy couldn't really stand up against the current Chinese navy (and against what the Chinese are currently building for the future it is even more of a joke comparison). The Taiwanese are fielding obsolete submarines because no country is willing to sell them modern D-E boats, and their current strategy is to rely on fast-attack missile boats armed with supersonic missiles to try and buy a day or three.
By the way China does have SSBNs. It has had one Jia class in service since 1981, and 2 or 3 of the new Jin class boats since 2010.
As for the PLAN not being good in logistics I think it is important to note that a prudent service prepares not only for what the probable enemy is capable of now, but also what the probable enemy will be capable of in the future. The Chinese, a scant 10 years ago, wouldn't have been able to do an amphibious assault against Taiwan. They couldn't be able to replenish at sea, or perform missions far away from home base. The Jia I was referring to above (there were originally two, and one apparently/allegedly was lost) was not even leaving base. In the last 5 years the Chinese have jumped leagues from where they used to be, and they are currently engaged in anti-piracy duties (read: training missions) far from base.
Anyways, to answer your original question, pound for pound the Japanese Navy is the second strongest after the US. Sure, it may not have the number of vessels the French, Brits, Russians and/or Chinese have; and they also do not have any vessels that are nuclear powered or carry nuclear weapons; but their vessels are quite advanced. The South Koreans also have some advanced vessels (their AEGIS class is arguably the 'best'), but they don't have the numbers of the Japanese. My number two in terms of pound for pound would be Japan, while my number two overall for now would be the French (like the Brits, but far more likely to use their weapons compared to the Brits, contrary to all the silly and dated 'wussy French' tripe one finds).
However, the clear future number two is easy ...China. By 2025.