I can give you a clear answer for MBB firms. The location of your office has ZERO impact on your staffing! The entire German system is treated as ONE office (with multiple locations, but only one stafing pool). Hence, it is completely irrelevant whether you are located in Berlin, Düsseldorf or Munich.
Regarding international staffing, McKinsey has a more global structure compared to BCG and Bain. In McKinsey, it is much more common to see completely mixed teams with, say, the leading Partner from Oslo, Engagement Manager from Frankfurt, one Associate from PAris and another Associate from Dubai serving a client in Saudi Arabia. In BCG, staffing for international projects would be more likely driven by the lead Partner's home office (independent of where the client is located). Of course these are just indicative descriptions and there might be many exceptions!