How might "The Tell-Tale Heart" be interpreted as a thematic father/son type of struggle for power and superiority?
Well, this would be the sickest form of father-son relationship, but the old man would be the weakened, but still-in-control father figure. The narrator would be the son who is struggling with his position and where he fits in, probably feeling a bit frustrated about not being able to operate the household by his own standards. After years of this, the resentment and frustration build to the point that the son cracks and focuses on one element of the father which drives him nuts--the eye. The ultimate act of seeking freedom and breaking out on his own would be to get rid of the object of pressure--the object that makes him feel less than a man. So, he murders the father and plants him under the floorboards of his own bedroom. Ta-da! Instant King of the House.
The narrator describes the eye of the old man as "The eye of a vulture" A vulture is a bird that flys above everything, so the eye could represent that the old man is always watching the narrator not giving him any freedom. He doesn't like having to share his house with his old father so by killing him he removes his "Always watching eye" and can feel free of it and have a clean conscious.
This however doesn't work because by killing the old man the police come over and it eventually leads to his own downfall.