I dont know about today, but tracking US SSN and SSBNs back in the seventies and eighties was a relatively simple excercise because of the excessive cavitation they tended to generate. In comparison the Oberons were much quieter. Saying that the reactors are quiet is not the issue. The battieries in a diesel electric boat are just as quiet. The drive systems are where the noise comes from, and most frequently this comes from the cavitation of the props. Because US nuclear powered subs move quickly, they cannot help but generate more noise. To be fair however the US subs had two priceless advantages....it could dive deep, very deep, and it could use exceptionally high speeds to extricate itself from a situation if the need arose. And in terms of attqack systems it was very advanced.
Common belief is that Soviet Subs are noisier than their western counterparts. This is true, but not for anythng to do with their reactors. They are not noisier because of their propulsion systems, so much as their drive systems are noisy. In particualr their props suffer from a lot of cavitation and this makes them easier to track. However, without the basic intelligence gathered about the signatures of each hull's special noise characteristics, it is is impossible to tell exactly what you are up up against, and what are the optimum frequencies to set your passive listening gear to.
And even though Soviet Subs are noisy, it is anything but easy to firstly achieve contact in the first place, but then, having made contact, maintain surveillance and not get detected yourself. Getting detected means that the excercise will be reduced to who gets the draw first, and thats basically a 50/50 chance of getting yourself sunk before them. Since the Russians have more subs than us (or did have), the math is simple....we run out of subs before them. So, from a western allied perspective it becomes imperative to maintain an undetected status to maximise our chances of a kill, and minimise the chances of them killing you.
Soviet tactics often involved the use of two subs....one acting like a beater (in a tiger hunt) , making a lot of noise and attracting a lot of attention, and a second operating in the shadows, and not so easily detected. Though only ever practised in excercise, I dont know how many times I have seen US Subs report that they have tracked and destroyed the enemy contact, only to be told they were sunk by the targets shadow. Maybe the Yanks got better at this game in the 90's, but they would fall for the same ruses again and again back in the 70's
Plus, a nuclear powered sub is an expensive and valuable piece of hardware. I never once heard of them being used to undertake the job of sitting outside Soviet ports and recording signatures. To do so they would have to operate inshore, in shallow waters, therby denying them one of their fundamental means of defence (their deep diving ability) Because they are nuclear powered, it would almost certainly have triggered WWIII if they had been detected. The Soviets back then would not have allowed nuclear subs that close to their main bases. We were confident that they never knew our Oberons were so close, but even if they had caught us, the worst thing would probably have been a stern message for us to bugger off. We were always careful to stay in International waters incidentally