As a current student myself, I have had several different types of experiences, both large and small. While it is true that larger companies are often well known and can look good on ones resume I feel that this is a superficial way of looking at this. A resume can help get you through the door with big names like that but with the more competitive job market it's what have you done, not where have you been. Companies don't want to spend the first three-six months training a new employee when there are others out there that already have gained the experience needed. With that in mind I am actually interning for a small consulting firm this summer which I expect to be incredibly valuable. Here, in a small firm I have the opportunity to interact with all different aspects of the firm; basically I'm not going to just be stuck in the accounting dept. marketing dept. etc.... One thing you can always do which sometimes can come off as pushy but in the long run is extremely beneficial: ask both firms what EXACTLY your internship will entail. From there both should  hopefully give you strait-forward answers which will aid you in choosing your internship

Looking at internships in the view of: will I get a job out of this?

This is also a very common way to look at internships when comparing large and small firms. I have a sibling who is interning at a large firm with the prior knowledge that if they do a good job they will have a job when they graduate. This is definitely more common in larger firms because in general they are doing more hiring. I would not say that it is limited to a large firm though because if you are working at a small niche firm they often have connections with larger firms. A previous internship that I had was at one of these small firms and this year as I began my search I asked my supervisor for advice and they gave me the names of some of their referral partners which were both small and larger corporations. In the end you can never be certain of if you will actually get a job out of an internship, all that you can do is learn as much about what each position will entail, who your supervisor will be, what your hours are, and lastly I'll hesitantly add on how much you will be paid. The reason why I am hesitant to add the last is because in the grand scheme of things if these internships are as high caliber as you say they are you will be destined for a job where you will be able to make quite a bit of money where the funds generated from an internship would seem insignificant. Hope this helps and good luck