Beyond the obvious, that the NSF Fellowship Personal Statement is "Why am I good for the NSF," and the Academic Statement of Purpose on a graduate school application is "Why grad school and why grad school?", how different or similar are the two essays?
Having already written an NSF Fellowship application, I'm now in the process of writing my Academic Statement of Purpose for grad school applications, and I'm trying to figure out how similar these statements are going to end up being.
There will be many common features, but the NSF has many highly stylized requirements, including "broader impact" and such, which would seem stilted or hypocritical outside that venue. NSF has a page limit, rigid formatting requirements, many other formal requirements, none of which matter in a statement of purpose. You have room to be more sincere, more genuine, explain more fully in your grad school application's statement of purpose. Also, unlike the NSF, where there is some compulsion to pretend that you already know what you're doing and will start research immediately, grad school applications (e.g., in mathematics) can easily and reasonably acknowledge that it might be premature to be thinking about PhD-level research prior to grad school.
(I don't necessarily hold a grudge against NSF over some of this, because they have to "make the sale" to Congress, in terms Congress-people can understand and find compelling, in order to get the money...)
