Startup internships tend to be semester-long job interviews, which means that you'll be doing the same thing that the full-time employees are doing but with more supervision at first. This is a huge win for you, the intern, for two reasons:
1. Instead of doing menial grunt work you'll be doing real work for real users, which is a _way_ better learning experience. Finding out what people want isn't something that can be taught. You have to make things, put them in front of large numbers of people, and see how they react. You can get this experience by building a startup and going on the long march of getting traction. Or you can work for a startup that already has traction and observe their users. The latter is obviously way easier.
2. If you're good you'll probably get a job offer right away instead of an option to take a job after you graduate. If you're the sort of person that needs a piece of paper in order to feel like you're worth something this might not matter. But if you're in it for the work itself, you can save yourself two years of salary plus tuition.
In a related note to point 1, work for a consumer-facing startup if you can. The way consumers behave and the way business customers behave are completely different, and consumers are a lot more fun to work for.