Reactor itself shouldn't be noisy. It may require pumps to keep it cool, which produce noise, but there was an article a few years back talking about 093's natural circulation when it comes to cooling of the reactor. So that's another aspect of noise reduced. Further noisemaker is usually the steam turbine. All today's nuke subs have one (or two, when it comes to older types) and one might try to somewhat lower the noise the turbine makes through very precise machinery. That's usually helped by computers, computer aided milling etc. All stuff that China is pretty good at, especially when compared to, say, 1980s levels of such tech in the West.
Further noise source is gearing mechanism, for which the same issue of computer and fine tolerances can be applied. Then there are various damping mechanisms inside the sub. Those aren't very high tech, one basically needs enough volume to make them work best. (which is why larger, nuke subs, can in some aspects have it easier to keep quiet compared to smaller subs). Basically rafts holding all the machinery separated from the hull, as well as flexible shaft joints and flexible pipes, serving as interfaces between any sort of noisemakers (such as the propulsion unit, Air conditioning etc) and any sort of fixed stations connected to the hull. Those were all first used in 1970s and 1980s and are a quite known quantity. It's unlikely their quality is somehow noticeable inferior to what the west had in 1980s.
What's left is the screw, which needs to be designed in a proper way, through computer modelling and made with fine tolerance milling machines, so the cavitation generation is kept to a minimum. The West started with those in 1960s but Soviets didn't really catch up there until 1980s. Again, an area that is unlikely to be worse than 1980s Western subs.
Basically, I see it very unlikely that current best variant of 093 is any noisier than the improved LA class sub. And may actually be even a bit quieter, since LA and improved LA class, due to political and doctrinal reasons of the time, did not feature natural circulation for reactor cooling.
The "Chinese subs are noisy" claim is something that is really outdated when it comes to newly produced 093 subs. It originated with 091 class which was indeed quite poor. And the initial variant of 093 probably didn't help either, as there are indications that the reactor design changed over time, thus allowing use of natural circulation.