I note there haven't been many responses to the questions, which rather surprises me (perhaps they sent messages directly). In answer to your queries (if you're still doing any work on HPL; it seems that those who do never really get away from it for long):
Imprimis: It varies. For some, it's the sheer perfervidness of the language, the rich textures and what some have called his "adjectivitis"; for others, it's the bleak vision; for some, it's his blending of real and fantasy, that is, his use of historical fact or actual legend/folklore blended with his own unique additions (e.g., the vampirism mentioned in both "The Shunned House" and "The Case of Charles Dexter Ward" as having taken place in Rhode Island is quite real, and an Exeter community really did exhume a body and burn its heart to prevent further such nocturnal visits as late as the 1890s; see Clauson's "These Plantations" and Charles M. Skinner's "Myths and Legends of Our Own Land"); for others it's the beauty underlying the horror. For some, it's the precision in dealing with often very subtle variations of fear, awe, dread, the mysterium tremendum, what have you. So, as said, it depends on the reader.
Secundus: The differences in Poe's style and Lovecraft's is that Poe was mostly concerned with the psychology of his characters and was much more under the influence of the late Gothics/early Romantics, whereas Lovecraft, for all his being influenced by Poe, was much more influenced by the essayists and poets of the 17th-18th centuries (Dryden, Pope, Johnson, Addison, Steele, Gibbon, Gray, etc.) and later Lord Dunsany and Arthur Machen, though he distilled his own unique style from the various influences.
Tertius: For me, it has largely become a blending of the philosophy underlying his work, the beauty of the vision and the often exquisite use of language, which I appreciate the more I read of his work; not only his stories, but his poetry and essays (which take some adjusting to). He makes one think, and ponder what it is he's saying, formulate one's own ideas much more clearly, and in general opens up vistas one might not have experienced otherwise. It is through my interest in Lovecraft that I've come to appreciate so many other writers and artists I might not otherwise have even known existed. I can always find something new and intriguing in Lovecraft; while the reasons his work still enthralls me may change (I'm no longer interested in the minutiae of the mythos, generally speaking, for instance), I'm always getting new levels of appreciation from his work. Some writers are capable of this almost infinitely; others are not. Lovecraft, I'd argue, is one of the richest because of his vast erudition and his intensely textured style.
Hope this helps. Best wishes on your pursuits.