I think that the best way to describe their relationship with each other is to say that they are, for the length of this story, at least, dependent on one another.
Clearly, Captain Torres is at the mercy of the barber. There is no way he could prevent the barber from killing him if he wants to. But the barber is just as much at Torres' mercy, though he does not know it quite so clearly. Torres could clearly have him executed if he wants to -- he knows (as we see at the end of the story) that the barber is a rebel.
I think that, at the end of the story, the relationship is one where Torres has the upper hand. In a way, he has proven that he is the cooler, braver man and I think they both know it.
Shaving with a long open razor blade is a highly skilled job requiring intense concentration: "taking pains to see that no single pore emitted a drop of blood." After lathering his customer's beard with soap, the barber begins to shave the beard with the sharpened razor. As the soap lather and the shaven hair collect on the long razor blade the barber will often pause and remove the lather by stroking the razor on his own bare forearm and will continue shaving. If he pauses every now and then to wash the razor he will take a longer time and more importantly he will lose his concentration.
Although, the narrator-barber is "secretly a rebel, he was also a conscientious barber, proud of the preciseness of his profession." So, the dilemma he faces now is whether to slit Captain Torres' throat or to give him a clean shave without nicking his skin. After quite a struggle within his mind he decides :"I don't want blood on my hands. Just lather that's all."
He puns on the word "blood" to ironically emphasise the fact that "he is a good barber. The best in town." Blood could either mean the blood when he nicks Torres's skin and collects it alongwith the lather on his forearm in which case he would not be regarded as an expert barber or the blood if he murders Torres by slitting his neck, in which case he would be branded a murderer.
The narrator is keen to be known only as an expert barber-only lather on his hands.
The reader is impressed and deeply moved by the magnanimity and the sense of honor displayed by the narrator and the relationship between the narrator-barber and Captain Torres can best be described as "the hunted becoming the hunter!"