I am trying to get into the habit of doing both. Handwriting for brainstorming/prewriting/outlining (whatever you want to call it), then typing what I've learned from that pen-and-paper exploration. That doesn't mean, to any degree, that what I type is the final version. I'm still discovering as I type, but I have a much better feel for what I'm trying to do. It's sort of like looking at a map before you visit a new place.
I also learned from my counselor that the physical act of handwriting activates the part of the brain that controls the ability to express thoughts via written word. So today's lack of pen-and-paper writing is allegedly causing people to struggle with writing in general. I have not done my own research into this, but I thought that was interesting. I tend to believe her, too. Just look at any thread of comments on Youtube...