We quip a lot about the disadvantages of large companies. There is, however, one major advantage: transfer opportunity (even though the formal transfer system of most companies should be a last resort; you're better off being requested) and the chance to make contacts. However, to actually get at that, you need to be a bit more "entrepreneurial" and self-motivated (to meet people and ask them about what they're doing) than the typical big-company employee.
Another upshot of this is that if you do it right, people won't fuck with you and you're very well insured against being personally fired or PIP'd. You might be laid off if there's a huge cut, and your boss might tell you that it's time to transfer, but personally firing someone who is well networked within the company is so politically dangerous that most people won't fuck with you.