The biggest reason to work at a big company is that you can have an opportunity to work on "stuff that matters" fairly quickly and you get introduced to ways of

The biggest reason to work at a big company is that you can have an opportunity to work on "stuff that matters" fairly quickly and you get introduced to ways of dealing with processes around working with important things, which can give you skills and confidence you might not otherwise attain. You're not going to acquire the experience of knowing what it's like to jump headfirst into fixing a build break during the runup to release on a billion dollar product unless you're working at a company that has a billion dollar product, of course.