I once read a fantastic book by Jack Falvey with a title like "Career Strategies After 35." It ponders the same question you posed. Its conclusion was "It is better to have worked for a large company than to work for a large company."
Working for a large company does bring several perks, e.g., larger salaries and name recognition. Right now it seems the company everyone wants to work for is Google. However, some career counselors report that for every company with millions wanting to get in, a corresponding number of people want to get out. (Once inside, they realize the Googles, Apples, Disneys, etc. aren't as great as they thought.)
Large companies like Google have become unattractive to certain people exactly for that reason -- it's become large! You'll be pigeonholed into one specialty, and it will be very hard to move across the company. Some people are more interested in creating the next Google, and to do that, they have to start small.
In a small company, you will be asked to do a lot more because of the limited resources. Yes, you'll probably get paid less, and also you won't have the name recognition, especially when you must job hunt again.
So you can form this compromise, especially nowadays that careers face so much flux. First, realize that no job is forever any more. If that large company wants to lay you off (as Yahoo will be doing this week), they can and will.
Conversely, you too can lay off the company when it's to your advantage. You can take the large company promotion with the PRIVATE knowledge that you will stay there as long as it's to your convenience. You'll get the benefit of adding LargeCompanyName to your resume. If you really do want to go to a small company, do so later within a few years. Nobody has to ever know of your true career goals and what you're up to. Meanwhile, get to know some small companies and get them to know you.
Second, realize that ours is still a brand-name driven society. Whether it's clothing labels or popular Web sites, brands hold a powerful presence. Even the allegedly "unbiased" in IT can't escape brands, including those people who hire in smaller firms.
Smaller firms have the disadvantage that they're not so known, they don't have their own brand. However, when they look for people, they too will be swayed by someone who's got a few name brands. And those small firms will also find it appealing when you approach them, when you somehow let it be known that as impressive as LargeCompanyName is, you find them even more impressive.