I honestly can't say that I can choose one over the other. I am always amazed at how Lovecraft can basically paint you into his stories with his detail and imagery. When I read his works, I feel like I'm looking the monsters of his stories right in the face at the end of the tale. And for Poe, I am simply amazed at how he can write such eerie tales (whether it be a story or poem) with such beautifully written language.
And, even though the two authors have very different styles, I have actually found Lovecraft's and Poe's works to sometimes seem rather similar in ways. That may also perhaps be a reason why I enjoy both of them so much.
I'll go ahead and mention some of my favorite works by each author...Some of my favorites by Lovecraft: The Dunwich Horror, The Hound, and The Outsider. Some of my favorites by Poe: The Raven (poem), Annabel Lee (poem), and The Fall of the House of Usher (short story).
I apologize that I didn't truly answer your question. I did ponder the pros and cons of each author, but I simply couldn't come up with a favorite when choosing between Lovecraft and Poe.
Best wishes!