There's also the 3rd option, MediumCo.
You can work at a company of 40-80 or so employees and have all the benefits of working for a big company without the red tape, politics, and inertia. If you pick a good one you can pretend you are working at a startup, but with better hours and a competitive salary.
I've worked at startups before and the biggest thing I've learnt is that a separation between owners and decision makers is a great thing.
The danger being that you rank up from being worth $30k a year to $60k a year (and convince yourself that this is great progress), while your buddies at BigCo have been stagnating in their march from $100k a year to $120k a year.
Seriously, though: like the mindset about focusing on career growth, but don't ignore BigCo. I personally couldn't stand working for one but you can learn things and meet people at BigCo, too. That's one of many reasons why so many people go with BigCo.