In the tell-tale heart there are several explorations of 'power'. It is the power of the narrator's guilt that makes him confess (it was all due to his mind), the power of killing a man for no particular reason (complete futility of life) and also the belief of the narrator that all things must eventually come to pass (fatalism), meaning first the death of the old man "the old man's hour had come" and then his own arrest.
The story shows the power of the mind--even the power of an insane mind. Having a son with a mental illness, I have witnessed the power of the mind to even convince him that I am not human. I have often wished that people with mental illnesses were not portrayed as dangerous to the community as that is a terrible stereotype to overcome. When I look at your question, I see the most important power as being the power of the narrator's mind which is the source of all the things which happen in the story.
Throughout the narration of his hideous tale, the narrator transfers power from the old man to the police to the beating heart when actually the really powerful horror is within the mind of the "nervous" narrator.
I think other editors make a wise point when they talk about the fact that the old man actually exerts a power over the narrator that he finds it impossible to resist. Firstly there is his "vulture eye" that haunts the narrator so terribly, and then there is the beating of his heart after he is dead. Even though the narrator exerts his power over the old man by killing him, he is unable to escape the hold of the old man over him.
There is also the power of the man's imagination (driven by his guilt) that he thinks he is actually hearing the dead man's heart beating and then pounding under the floor boards of his house. People can have creative ideas, but it takes a powerful imagination to make them that real.
While I agree with the above, I would like to offer another side to the division of power in the story.
I would have to say that I believe that the old man does have power. His power comes from the fact that his eye forces the narrator to commit murder. I would have to say that a person would have to have great power over me in order to get me to murder.
The narrator believes that power is in his careful execution of his plan to eradicate the old man's eye and hide the body. In his insanity, he believes that he is able to control his actions and emotions - see how he boasts about the repeated extensive observations he makes of the old man - yet it is his unusual behaviour which reveals his bizarre crime.
The narrator's desire for complete control--and particularly of the old man and his evil eye which so bothers him--leads him to commit his evil deed. He believes that the elimination of the old man, and the successful dismemberment and hiding of the corpse, will ease his extreme nervousness--his madness--and give him complete control over his life within the house.
Ironically, although the old man is indeed objectively powerless, somehow the narrator feels threatened by him (particularly by his eye), and therefore the person who actually possesses power feels threatened by the person with no power. I hadn't thought about this paradox before, so thanks for posting this thought-provoking question!
The narrator is powerful and the old man is powerless because the narrator is unstable enough to think that the old man is dangerous and kill him in his sleep. The police have the power to arrest the narrator, but the power of his guilt is stronger.