In "The Tell-tale Heart," the murderer (narrator) works himself up into a frenzy before revealing his crime. His loathing for his victim and his fixation on the victim's eye is a morbid fascination pushing him into a state of hysteria. As mentioned in the previous comment, the hallucination he experiences (the audible,then loudly beating heart) reinforces the certitude of his insanity.
In "The Black Cat," the murderer (narrator) ultimately expresses regret and even self-revulsion. As he is going to be executed the very next day, his narration of the tale is his confession. Some people interpret that the 'listener'(reader) is in the role of a priest, there to hear his sins and give him absolution.
The initial effect on the murderers is relief to be free from their tormentors. In "The Tell-Tale Heart", after he murders the old man, he relays his relief: "His eye would trouble me no more." In "The Black Cat", he says, "My happiness was supreme!". This relief soons turns to cocky egotism at the cleverness of their crime, at their assurance of having covered it so well, they would never be caught. In "The Tell-Tale Heart, the narrator leads the cops into the room of the murder, and "in the wild audacity of my perfect triumph, placed my own seat upon the very spot beneath which reposed the corpse of the victim." In "The Black Cat", the narrator brags to the cops about how well the walls in his house are built, and "through the mere phrenzy of bravado, I rapped heavily, with a cane which I held in my hand, upon that very portion of the brick-work behind which stood the corpse of the wife of my bosom."
The effect of this bravado and egotism in "The Black Cat" leads to the discovery of the murder. In "The Tell-Tale Heart" it is the narrator's own hallucinatory guilt that reveals his evil deed. Up to that point though, the after-effects of their crimes are remarkably similar.