I have never interned in a startup environment, but I can provide some insight into what it's like to work for a corporation. I participated in my school's coop program, which allow me to work at IBM for ~9 months in programming/design. Working in a corporation is everything you expect: very slow, process-oriented, very little responsibility. Doesn't matter how hard you drive your manager for work, it's unlikely you will get anything substantial unless you take the initiative yourself. I can't say I learned a lot in terms of hard technical skills (you will learn much more in school), but I have learned some very valuable soft skills -- how to coordinate work with others (it's surprisingly difficult when you are only coding a small piece of work that belongs to something much larger), how to present in front of senior managers, etc. One of the most valuable lesson I learned is to comment your code, I remember back in school, my professors tried to drive that concept into our heads, but I always thought, why do I need to comment when I know the code by heart? Nothing makes you realize the importance of comment until when you try to debug someone else's code, and the genius name variables after his children (serious, no joke).
There are valuable lessons to be learned in a huge corporation. They are procedures, how to coordinate work, how bureaucracy works, and the most important lesson I learned is -- I dislike it and I will never want to program in a big corporation environment.
From what I have heard and read, you will learn much more in a start up environment. You may not just do programming or design, but you have the opportunity to get involved with marketing, advertising, etc. But at the same time, you won't see the picture of what makes corporations successful at what they do. If I have to do it all over again, I would probably intern at a start up because there are more learning opportunities. Corporations are very silo-ed, every department operates on its own and it's very hard for interns to touch any other pieces of work. (e.g. if you are a programming intern, chances are you won't have a chance to do marketing as well).
I think in the right sort of corporate environment, a bit of initiative can give you a lot of opportunities the less-motivated might not have (or want). You also can learn how to work in a team, and probably have better hours than your startup counterparts, giving you more time to work on outside projects--such as your own startup--or in general to just have a life, meet people and pursue hobbies.
I like having some distance between me and management when I'm working as an employee, because then it doesn't grate on my nerves that I'm not working on my own startup while watching someone else run theirs, with the knowledge that they're using me to make their own dreams come true. I'd rather not see that, and in a large organization you don't have to because they're somewhere else, in a different building perhaps, or political appointees, for example.
There are valuable lessons to be learned in a huge corporation. They are procedures, how to coordinate work, how bureaucracy works, and the most important lesson I learned is -- I dislike it and I will never want to program in a big corporation environment.
From what I have heard and read, you will learn much more in a start up environment. You may not just do programming or design, but you have the opportunity to get involved with marketing, advertising, etc. But at the same time, you won't see the picture of what makes corporations successful at what they do. If I have to do it all over again, I would probably intern at a start up because there are more learning opportunities. Corporations are very silo-ed, every department operates on its own and it's very hard for interns to touch any other pieces of work. (e.g. if you are a programming intern, chances are you won't have a chance to do marketing as well).
Hope that helps.