The answer, as it often is (at least when I'm answering) is: both!
Honestly, though, the best answer I ever received to this question came during a workshop I attended at the Ocean State Writers' Conference. (The first writers' conference I ever attended, back when I had just started dabbling with short stories.) The author who was presenting was asked this question and he replied that when he drafts, he starts with an idea (character, place, question) and it's as if he is driving on a highway at night. As he drives, his headlights (writing) illuminates a new sign and he can tell where he is, where he might go. But in between those signs, it's all dark.
Though I've drafted many different ways (sometimes starting with a firm idea of where I wanted to end up; sometimes with a full outline), this is still my favorite method. Of course, it necessitates additional drafts because the intention/motive/goal of the piece only comes out as it is in progress; you have to go back and clear up themes and the central "strings" of the piece. But what piece of writing can't benefit from that practice?
This question has been on my mind as I've begun a new rough draft of a piece I've worked on multiple times (I have two full "fair" drafts of it) over the past three years. In doing so, I'm undertaking a very different style of composition. I have those two full drafts lurking in my mind -- that's a whole bunch of road signs! But I want to start fresh... I want to turn off that route (or not; I want the ability to deviate. What's new?).
The process of trying to do so -- trying to let the story head in a new direction, trying to let it feel its way through itself -- is proving difficult, but it is also emphasizing to me that this is my preferred way to draft. Not quite "seat of the pants" but close! That's where the possibility and imagination can really bubble (and then, through rewriting, ferment). Since I've been thinking about this lately, I thought I'd share my thoughts on the process.
What is your preferred method?