we don't know what the real noise levels of the subs are. In peacetime, you like to keep that from potential gatherers, so you will need to obscure your real signature, even if it has to use noise generators. Personally I don't think they are as quiet as the latest Western sub designs, but nonetheless they are featuring some modern quieting features such as closed limber holes, anecholic tiles and skewed propellers, so their technology level is right up to the LA-Akula class of boats. Personally I must also add that Chinese subs appeared to have improved rather late---2004 is the crucial year. That is why they are all of sudden in a major build surge starting only from that year. Previous to that year, their designs have been hit and miss, testbeds with issues that need working out. The discovery of the Yuan was a major surprise for everyone in that year, since it has become questionable that the production and movement of the subs can be tracked.
Soviet subs have some noise issues that come from design decisions the Chinese are not sharing. For example, many Soviet subs have twin reactors, while US and everyone else submarines, including the Chinese, only have one. (There is only US SSN ever to have two reactors). Many Soviet subs also have two propellers and still kept that arrangement when US subs have shifted from two propellers to a single one (despite Rickover's objection).
So when you have two reactors, two reduction gears, two driving shafts and two props, you will make at least double the noise compared to a set up where you only have one of each. The Chinese nuclear subs don't have these issues; they all use single reactors, single prop arrangements, even with the Han and Xia class. If it is true that the 093 and 094 class have turbine electric drive (an idea the French used with their nuclear subs), by all means expect to be a bit more quiet since they removed one noise making factor and that is the gearbox. Do note the considerable French flavor in the PLAN development in other fields.
Lets compare the Songs and the Yuans against the Kilos, for example. The Kilos, like many earlier and small conventional submarines, don't even passive low frequency flank sonars that are used for long range detection. But the Chinese had the foresight to add them to the Song and the Yuans. The Russians never had passive flank sonars on a conventional until the first Lada class came out, so the Chinese actually beat them to it. The latest Google Earth measurements put the Songs and Yuans right to the size levels of the Collins and Oyashio class, among the largest diesel boats built and size helps in making a sub quieter. Frankly there is not a lot of diesel boats with passive flank sonars, because of space issues, and usually it is the few bigger diesel boats in the world that do. You also need to put your diving planes in the sail so the planes won't interfere with the flank sonars, which is one reason the Kilo is a bad design to put a set of flank sonars.
In addition to that, by having more space in the Song and Yuans, there is more room for batteries, which means more electrical power for sensors and command centers, and more room for reloads.