If I get an internship at a big company (Google, Facebook, etc) I think I would have structure, but less responsibility. I would have access to a ton of smart people, mentors, other interns and resources. That said, my contributions would be an incredibly small part of the company.
If I worked for a small startup (Swigme, Coaster, Looker, etc) I would have more responsibility. I would see directly how my work effected the product, sales and company. But I would be in a much more isolated environment. I would probably be exposed to less successful people, younger people, and less people.
A medium size company (Dropbox, Evernote) would provide the best of both worlds. Or the worst of both worlds. I cant tell.
It depends more on the specific company and leadership team. And not just the company size.