A few years ago, when I was a Cal undergrad, I turned down an internship at the larger company you're referring to. More specifically, I already accepted another offer by the time they called me back. I work a few blocks away from there now, and when I walk by the campus, I sometimes still wonder whether I'd be in an entirely different branch of the industry if timing on that phone call had worked out just a little bit differently.

As others have mentioned, the company's size is far less important than the quality of the people you will be working with directly. This site has a decidedly strong bias towards do-it-yourself, but to me, the point of an internship is to acquaint yourself with people who are a few years further down their career path than you. They've been in your shoes and can help guide you. Try to figure out which boss or coworker will be a better mentor. You'll have plenty of opportunities to strike out on your own after you graduate.

@njoubert - could you email me please? I'm about 120% certain I can help you a lot w/ this decision. Email is in my profile.