Let's see who's still being read in 200 years.
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Poe wins as his work has been around longer. Stephen King came along 100 years later.

Poo
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Poe. No contest.

I think King was for the most part a pulp writer of genre fiction. His adult fiction could be great (Rita Hayworth and Shawshank Redemption, The Body, Dolores Claiborne) but mostly he was interested in the style of EC Comics or Famous Fantastic Mysteries and bringing it to everyday Americana settings. King was obviously influenced by Rod Serling and all those 50s sci-fi horror authors he would have grown up reading, along with HP Lovecraft.
I don’t think he has the literary substance of Gothic/Romantic writers like Mary Shelley, Poe, Bram Stoker, Henry James, but nor was he trying to be. King is very much a postmodernist who took all those various influences and repackaged them into blockbuster form for the mainstream, and did a very good job at it.

For storytelling, understanding what his readers want and giving it to them, and with interest, Stephen King, easy. However…
Edgar Allan Poe as an artist, a poet, the man who invented horror as we know it as a literary
genre
,–and don't let's forget the detective story–this man far surpasses King as a writer; especially at the level of a genius. Poe towers over King.
In King's favor, as a man and writer: he's kept his physical and mental health, managed not to drink or dope himself into early oblivion and death. Yet capable and gifted as he is, Stephen King is a shallow writer.
Also against King, and in my opinion, King has never been able to, call it what you will– grow, evolve, achieve–the maturity as an artist to write fiction as an adult, for adults, that addresses adult issues. There's something of a grownup teenager to the man. Yet this is part of his charm, as author and human being, and I suspect, at the core, of his popularity a well.
Mr. Poe appeals to a wider audience because he deals with a wider range of issues, he flirts with perversity, and weirdness generally, while one can't but sense that when Stephen King channels the perverse, the Uncanny, that that's part of the product he has to sell. King is a capable and brilliant essentially popular writer. He writes for the Common Man, makes no bones about it; while Mr. Poe aimed higher, much higher, and this clearly was his goal.
Both men, as authors, got where they wanted to go in life
as writers
,–with King lasting much longer–Poe achieving far more as an artist. I say this with no malice toward Stephen King.
This is a discussion and evaluation of two famous writers; it is not, nor was intended to be a making of invidious comparison between these two highly gifted men; men with different strengths and weaknesses. I'd just as soon leave it at that.

Edgar Allen wrote some decent stuff and led the way to modern horror, but he never grabs my full attention like Stephen King does

Edgar Allan Poe is better. He set the writing standard.

King. The much longer lifespan; the incredibly richer body of work; and the fact that Sai King exists simultaneously with cinema.
That being said, without Poe (also Lovecraft and Bradbury), the Stephen King we know and love would not resemble the prolific writer we enjoy.

The Constant Reader.
Without Poe, Lovecraft, Bradbury, and Matheson, Stephen Edwin King would have been influenced otherwise in a literary sense.
Scary thought, isn't it?

Watch this, very funny:

King not even close
Poe doesn't even have enough material to cover what King has covered
and most of Poe's stories pale in comparison to King's length wise or when it comes to character development

King, undoubtedly.
Life can be arbitrary and comes without a warranty.

So let's take Poe to the Pet Sematary, then see who wins the fist fight.?

In a fist fight? Definitely King. Poe's a corpse, after all, and after all these years, not to fresh either.
Life can be arbitrary and comes without a warranty.