Not so long ago news stated that an Indian Navy, Russian-build, submarine was able to "sink" American Los Angeles-class nuclear submarine. First of all congratulations. This is a fantastic propaganda news for Indian Navy. Not that I have something against them. Opportunity to train and practice finding and tracking enemy submarines is priceless and might become handy in case of any future conflicts.
Kilo-class submarines are very capable and quiet vessels. The biggest advantage over nuclear powered submarines is the ability to go extremely quiet by, literally, switching off everything. Nuclear subs cannot turn everything off, reactor must be cooled at all times and cooling system, even though quieted, makes some noise. Newest Kilo-class units are extremely quiet.
As I said it is a great success to sunk a nuclear submarine but.... There is always a but. Los Angeles-class submarine are old vessels. This particular one was commissioned in 1983 this makes her a 34 years old vessel. Quite a lot for a submarine. I bet that Virginia-class or even better Seawolf-class submarine would never be found. Those type of exercises should be held as often as possible because it is a great opportunity for allies to train and gain experience.
I am, however, pretty sure that the outcome would have been different if it was a Virginia-class sub to take part in that kind of event.