Promotions and Making Partner: How does it vary between the Big 3 and Geographical Location?

I am interested to know if there is any data or consensus as to how different firms and maybe how different offices affect the speed and probability of promotion and chances of making partner.

First, across the Big 3 MBB.

I've heard that McK is more "cut-throat" and "intense" than BCG/Bain, and their retention rate (anecdotally from speaking to a few couple people) are much lower than BCG/Bain. If one is interested in a longer-term career and seriously trying to get to partner or as close to it as possible, would this then imply it is more difficult to get promoted to partner in McK than BCG/Bain?

Next, across geographical locations.

I'm guessing like many other jobs, "nice locations" like NYC, Boston, San Francisco, etc. have way more demand than "sub-par locations" like Detroit, Atlanta, etc. Please, take no offense if you don't live in a "nice" coastal city, but that's just a majority mindset which is in no way consultant specific. If that's the case, does that mean that the more "desirable" office locations are staffed more competitively, and thus making it more difficult to get promoted to partner?

Please feel free to discuss, and shoot my ideas down if they are not making any sense.