That is how I am. I wish I had the willpower to do what you do, VeeLynn, and keep the story to myself until I'm almost done because it's nice to give yourself that flexibility to go back and edit, incorporate new ideas, and make sure it's perfect before you post.
I am more like Mare, though. I take a lot of time before I even start a new story to think it through and at least start to outline it; I never actually start writing until I have at least a general idea of where the story is going and how it will end. Once I start writing, I try to get a few chapters written to make sure the story is flowing well and turning out the way I want it. If I'm confident in what I have and confident that I'll be able to continue it, then I post. I enjoy posting stories as I write them because I like that ongoing feedback; it keeps me motivated and on track and sometimes gives me new insight that helps me write the rest of the story better.
My problem right now is, I'm sitting on this new story I technically started last summer, but have only been making real progress on for the past week. I finished Chapter 1 over spring break a week ago, and I'm on Chapter 5 now, which is pretty good progress for me lately, since I haven't been able to write consistently on anything else since I finished Curtain Call. I'm getting to the point where I'd like to start posting it soon, but at the same time, I feel bad doing it because I have two other unfinished stories that I really should be writing instead. I don't know what's worse - adding another fic to my list of stories that need to be updated, or just not updating at all.