I decided to join a startup right out of university. We were later acquired, so now I've been working at a big corporation for just over a year. There's a few dimensions to think about when making your choice:
Personal growth: At a startup, you'll probably learn a wider variety of skills, but you may not learn any 1 skill as deeply as you would if you specialized at a big company. So far in my experience, at a big company it feels like it's easier to fall into a boring, predictable pattern and stop learning new things.
Money: If you're joining an early-stage startup, you'll probably have a lower salary than at a big company but you'll have significant equity in the company, which can lead to a big payoff if the startup takes off. You should think of this a bit like gambling, since most startups will fail.
Time: Usually, startups are more demanding of your time than big companies (but definitely not always). Since people at startups are so heavily invested in the company, I feel like they are more willing to work long hours to make the company a success.
I personally think it's smart to join a startup while you're young for the following reasons:
-It lets you try a variety of roles and skills to help you figure out what is the most fun for you.
-You have more free time to devote to long hours when you're young than when you're older and have a family.
-The risk of the startup failing (i.e. you lose your job and have no paycheck for a while) is much scarier when you're older and you have kids, a mortgage on a house, and so on.