Why is the difference in US,western building concept of the sub compared to Soviet thingking?
What are the advantages n disadvantages of each style of construction?
Its a challenge to answer in a nutshell some of their notable differences.
US: Started with double hull design but sometime afterwards switched to a single hull design from the Skipjack onwards. USSR: Stayed with double hull design.
West: Shifted from double shaft, double screw designs to single boresight shaft, single screw designs in all submarine types. USSR: Although it took longer, finally did the same except on SSBNs, where they remained double shafted, double screwed. Until the Borei class that is, but the Borei is post Soviet Union.
Reactor: West: By far single reactor designs with few exceptions like Triton class. USSR: SSBNs are all double reactor. SSNs started with double reactor designs then shifted to single reactor.
US in particular from Thresher class onwards: Uses spherical sonar dominating the nose dome. Torpedo tubes are moved elsewhere. Seawolf added chin sonar with spherical sonar. USSR: had the standard layout with torpedo tubes on the upper half of the dome and the chin cylindrical sonar on the lower half of the dome. Allegedly moving to a spherical sonar design but that would be post SU era.
On diving planes, both started with retractable ones in the hull. From the Skipjack to the early LA class, the planes are moved to the sail. From the 688I onwards, moved back to the hull. The Soviets always had their planes in the hull except for the Delta class. SSKs are a different matter as they have another reason of moving their planes to the sail which has to do with flank sonars---hence why SSKs trended to put planes in their sails as the nukes kept them to the bows (Artic ice breaking among other reasons).
On the sails, the US seems to prefer fairly squared designs. The USSR is divided into two camps. The Malachite bureau likes streamlined, flaired sail designs while the Rubin bureau likes them squared too.
Towed array. In the West, sometimes they're pulled from the hull, either top, underneath or the side using a sleeve. The Russians like to pull them from a tail extension on top of the upper vertical fin.
Limber holes. The USSR likes them in lines of holes, while Western designs prefer slits.
Cruise missile: The US has them vertically launched, the USSR has them on an angle. The Klubs are VLS but they're post Soviet Union.
As an added note, the Western nations also have some differences between each other, like between the French, US and British nukes. Western SSKs also seem to differ in their approach, e.g. Scorpene vs. Type 212.