May be because the diesel sub work on battery most of the time. diesel engine operates only at the time of charging of battery. Am I right or wrong?
You must compare comparable things !
A SSN is able to run at more than 25 knots (and some even much more) during weekss...
A AIP SSK is able to run at 5 knots during 1 or 2 weeks or 20 knots during some few hours.
A classical SSK is able to run at 5 knots during few days or 20 knots durinf few hours.
A SSN cruising at 5 knots is probably as stealthy as another modern SSK, with or without AIP, because what is noisy in a nuclear reactor? the pumps. And a lot of modern N. reactor can run at small power (ie 5 knots) without pump, but using natural convection.
So at small speed I think all are very quiet.
At high speed, more than the pump, it's the hydrodynamic noise that prevails. So no classical sub advantage.