Twain's story seems the more obviously funny of the two. Most people tend to read "The Tell-Tale Heart" as a scary piece of short fiction in which an innocent man is actually killed by a maniac. (For more on this view, follow this link: http://www.enotes.com/tell-tale-heart/critical-overview)
Twain's tale starts off seeming a bit scary, but it quickly devolves into farce, as when the narrator says to the giant,
"Now what sort of a way is that to do? First you come lumbering about the place bringing a legion of vagabond goblins along with you to worry me to death, and then when I overlook an indelicacy of costume which would not be tolerated anywhere by cultivated people except in a respectable theater, and not even there if the nudity were of YOUR sex, you repay me by wrecking all the furniture you can find to sit down on. And why will you? You damage yourself as much as you do me. You have broken off the end of your spinal column, and littered up the floor with chips of your hams till the place looks like a marble yard. You ought to be ashamed of yourself -- you are big enough to know better."
I would tend to agree with the position that littleteacher takes on this subject. The believability of the narrator in both stories forces a reader to question their reliability. Even with the question of reliability, one cannot get away from the movement of the story and the curious tale being told.
Thank you! Your ideas are very helpful.