The single biggest advantage of a large company is resources — of all kinds. Money-wise, while large companies do generate a lot of overhead, they also have the money to cover it. That manifests itself in all sorts of ways. If business slows down, you still get your wage at the end of the month.
Cons
With all of those resources and processes come bureaucratic red tape. You’ll have a tough time having any ideas heard, let alone ones that are outside your pay grade that you think might improve “the company” as a whole. The larger a company gets, the more risk-averse it becomes — deviation from standardised practices is rarely tolerated.