This is hard to say, as it truly depends on the office, the leadership you're placed with etc. etc. That said, in general, you should expect a wider range of projects, a more extensive network, and a bit of a "tougher" culture in terms of intensity and feedback. Bain is known a bit more for it's "A Bainee never lets another Bainee fail" whereas McK is known for being a bit colder.
Regardless, try not to focus too much on generalizing statements on culture (like the one I just made!). Rather, make the best of where you are - you'll find there are good people everywhere!