C'mon, admit it. That's the question all you writers really want to ask your favorite bestsellers. I can't speak for them. But I can tell you about my process—I do both.
When I started, I scratched everything out by hand, an illegible crablike scrawl. Later, when I worked as a journailst and corporate writer, speed against deadline came to matter as much as content. So I learned to type from start to finish.
But now, I'm back to handwriting. Almost all my first drafts are done by hand in a Piccadilly Notebook (the poor man's Moelskine) using Precise V5 marker. Then I type thos drafts into the wordprocessor. And start again. (Black coffee is optional but highly reccomended.)