Me, I think my strongest skill is in making my characters seem like real people. To me, that's one of the highest compliments I can be given about my writing--though it also helps if the story is paced well, and the plot is good and believable!
I think I write dialogue well, and I like my writing best when my characters have to think about things during the story, when they have to ask themselves important questions. David Gerrold once said that the best stories are those in which the character has to make a decision, rather than merely fight something. I agree with that. I've had at least one character darn-near want to commit suicide because of a bad decision he made. That's the kind of drama I like to have in a story, though not a constant diet of it.
The writer at whose feet I worship is Lois McMaster Bujold, because that woman can plot her way out of a tesseract. She is brilliant. For truly gut-wrenching drama, I like Susan R. Matthews, but you have to have the stomach to read her work. I personally have not gotten past chapter 6 of An Exchange of Hostages. I am dreading the later chapters. C. S. Friedman is also good. From page 1 of In Conquest Born, I knew why her two protagonists would want to kill each other throughout the book. She is also a brilliant writer.
Someday, I hope my writing will be as good as theirs.