I believe this is the short story Wake Up To Thunder by Dean Koontz. It can be found in the short story collection Children of Infinity edited by Roger Elwood (1973). I remember reading this story back in the 1970s. When the Matrix came out I immediately thought of this story. I don't know how it got away without a copyright fight.
As a note, I do believe this is the only collection in which this story is available.
Wiki Dean Koontz Bibliography
Discussion on similarity to Matrix
Second Discussion on similarity to Matrix
In it the occupants of the hive are in a matrix like environment. However, instead of being used for energy, their combined minds feed the AI "Thunder" which evolved out the sleeping masses.
The actions do not actually take place on a generation ship. Instead the Hive exists on Earth. However, there is a starship component in the story which is what you are probably remembering.
The quote you are remembering when the Policeman takes on the Renegade is:
"We clutched his bare flesh. I felt my fingers on his throat, felt his windpipe crumpling as I pressed. Then I went for him with my teeth. I was sure Thunder watched. I was sure he knew. He would love me the more for my fanaticism."
As you have already listed the spoiler for the story, you are also correct that the Policeman eventually becomes a renegade like the ones he had previously hunted for Thunder.