Currently, Russian Delta and Typhoon class subs are fitted for very long operations so a pool, sauna, gymn (?) and pet are are provided along with larger quarters, I think, to allow the crew to withstand a long patrol or under the ice in the Artic.
A bigger ship with 400 crew allows much more in the way of science and sensor capabilities. Computers are more extensive Adequate room is provided for two person cabins for crew and junior officers and single cabins for senior officers.
You have the bowling alley, the forest area and the Olympic swimming pool and large cargo facilities.
You also have more power availible for shields and weapons.
These crew amenties, like on Russian ballistic missile subs allow the crew to not just endure but enjoy their surroundings on a long patrol.
Oh, there are self preparing resturants onboard also.
Finally, a sufficently large shuttlebay is there as well.
Check out US and Soviet Submarine Designs of the Cold War 1946 to 2006 just out and authoured by Norman Polmar, an acknowledged expert in naval vessels with illustrations by A.D.Baker III, an expert in ship drawings.