I began my career at startups (my office was the dining room!) and am now working for a Fortune 200 company. Startups are great at the beginning of your career because you play so many roles: developer, architect, product line manager, marketing manager, etc. The problem is this period in a startup's life is short-lived: traditional roles are quickly established and the defending of turf begins. So you're not going to avoid politics for long. On the upside by being small you can move very fast, that is until you're successful. Success tends to be an albatross - management becomes reticent to change things.
Big companies have some advantages people don't often think about. They have the financial wherewithal to invest in new technologies and methodologies. They can also afford to send you to conferences and interact with your colleagues. Yes they move slower, but success doesn't become an albatross - they keep moving.
It's the classic tortoise and the hare story.
Another thing you may want to consider is advancement. You tend to advance faster at startups and can attain more responsibility. That allows you to transfer in to a higher position in a big company later down the line. The fastest way to advance at a big company is to go to a smaller company, advance, and come back. Depending on your career goals you may or may not be interested in this aspect.
