Pros
Has a ton of resources, does not overreact to small upsets as is fitting for a private company. Has a ton of smart people and comfy offices, and great information resources. Will generally provide you with space to breathe. Has a big name, plush insurance benefits and a unique stock sharing plan. You'll probably get some interesting assignments along the way.
Cons
You will be a small and expendable fish in a big pond. Large and inflexible corporate infrastructure with many inscrutable management practices. Tends to focus on the patina of engagement rather than developing truly engaging leaders with truly engaging missions and applying its employees to interesting problems and developing resilience. Has a strong "run by corporate HR" flavor you might not expect from a private firm.