AIP is also possible with fuel cells like on German Type 212/214/Dolpin submarines. The only moving parts are the small pumps to deliver the fuel.
A nuclear reactor can't be shut down immediately. Reactors need cooling pumps all the time pushing a huge amount of water through the submarine.
Here is something to read: http://seefahrer.blog.de/2013/04/11/manoevertagebuch-westlant-deployment-07-08-15746059/ (You can switch to English on top right)
From that maneuver I conclude German Type 212 u-boats are quieter than US “Los Angeles”-class submarines.
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