I think I’m more of the 1st. I like to know EVERYTHING about my characters and really make them seem real. I have tons of character ideas, but when I want to write about them, I have to come up with a quick story, which I don’t like to do either. I like to know the details of both, but like I said, I usually come up with characters first (it comes more naturally).
For me it tends to be a mix of both, but I tend to develop the story first and then develop the characters that would be a part of it. I tend to have both fairly developed by the time I begin writing my actual story, though.
I usually start with a mood, build that into a setpiece (usually the climax or very beginning of a story) with arbitrary placeholder characters, and then try to reverse engineer a plot in both directions. As I write the characters into scenes, they take on a life of their own.
"...the one with whom he so sought to talk has already interceded for him." -The Master and Margarita
Nice to know I’m not the only one who starts my stories at the end…or at least at the climax. I often have that “big scene” in my head, and then, to create the story, work back from it to what seems like a good beginning point.
However, now that I’m a couple of books into my series, the main characters are much more fleshed-out and I have a much better idea of how these particular characters would move themselves toward the scene the story’s really all about. So it’s a lot easier.