NYU is a huge school with a fantastic reputation. It has a lot of international students, and is in a lively part of the city. It attracts top-notch professors. It's a very liberal school. It's a very difficult school to get in to. With so many specializations/degree programs, there's a ton of diversity, which can be good or bad, depending on if you want to basically be surrounded by like-minded students in your own field of study.
Parsons is a school for serious design students, not a party school at all. There's a lot of competition among students, but I've found it to be a motivator instead of a hindrance. Having a degree from Parsons will open doors career-wise, especially if the student wants to work in NYC. They have a lot of professors/instructors who have actually worked in the field, with success, and not just text-book professors. Parsons has a much less student:instructor ratio than NYU where you can have 300 students in one class.
Both excellent schools. If she wants to focus on design and eat drink and sleep it, Parsons is for her. The students there have real ambitions.