Neither will get you a job in strategy or consulting in Germany.
McKinsey definitely will require that you speak German to get a job in Germany.
BCG is less strict with language but also expects top school graduates. Neither of these schools would be good enough for them. They hire their German MBA graduates from higher-ranked schools in Europe.
Now talking about boutique consulting. They usually have smaller businesses as customers. German language is even more important as these customers don't deal with non-German speakers that often.
Your possibility of becoming a consultant, either in-house or in a professional service firm is very bleak. Better know it now before throwing in your money, not to mention both Mannheim MBA and ESMT MBA have lame career services (check FT ranking, tick only the career service rank item). You are most likely to end up in a fintech startup in Berlin.