I think that in general, the way to win NSF is fairly different from winning NDSEG. NSF is much more transparent about their process and they are looking for specific things: broader impacts and intellectual merit and all that they encompass, diversity in a variety of forms (e.g. geographic), and other items. As a result of their process being more transparent, there are alot more tricks you have to know to totally play defense and prevent yourself from giving the reviewers an excuse for a rejection.
NDSEG seems more cut and dry. They don't give you feedback, so the process if very opaque. They claim to have some selection criteria, but I don't know how strictly its used. I would be unsurprised if there were quota's and cutoffs based upon GPA and school. In other words, the fellowship is less holistic, which I think is unfortunate and ultimately not the best way of selecting students.
A big problem with both fellowships is when students' advisors just write the research statement, or the writing is pulled from their Prof's research proposal. At least for NDSEG, this advantage is less unfair since there are just less tricks to be incorporated.
However, I'm interested to hear how people wrote their applications. I was an NSF winner so maybe I'm just less familiar with this fellowship.