I've encountered two enemy subs so far. From both experiences, I have to say that subs don't like to let you know you've scored critical hits on them. Both of my kills had submerged in an attempt to get away before slowly sinking, and presumably experiencing pressure breaches and the like.
First on caught me off guard, time compression didn't revert to 1 when he came into range, so by the time I was preparing to attack, he was in the process of diving. Managed to track him down using the hydro, and once he popped up, I laid some deck gun shells into him. He submerged a final time, and confirmed his demise with the external cam.
Second one was a friggin funny story. I knew there was a submarine in the area and was pretty damn close to me, so I decided to dive and try to track him down using hydro. Soon enough, I hear screeching and metal grinding. I am at about 100m down and take a look through the peri, and me and this damn Brit have locked our subs together....so I did the only logical thing I could think to do...and since I was under him and he was stuck on my conning tower.....
BLOW THE BALLASTS!
We eventually make it up to the surface, and I jump on the deck gun to finish him off before his sub slinks off mine, and he falls down to the bottom of the sea.
Despite my fun experiences with subs so far...none of been really aggressive towards me, and I'm a little disappointed. Seems like the enemy subs just run away all the time. But oh well.
Oh, and I have video proof of the second story

at least the part where I force his sub to breach out of the water. Lol