Non competes are - generally - unenforceable anyway (or very hard and expensive to enforce); courts enshrine free competition, and (at the end of the day) your Human Rights, guaranteed under numerous European conventions would be infringed by limiting who you could and could not work for. There are exceptions - for example someone from Lockheed might be exluded from working for a competitor in another (not allied) state, as there are national security interests which override the free state point. But this will not apply to LEK/BCG. Even if your contract stated that you could not say move to another consulting firm to undertake the same specialised work this would be very hard to enforce - your current employer would need to prove in court the move was damaging to their business.
The clause you refer to is simply boilerplate stuff to prevent you disclosing sensitive client information you may have access to, but as a professional person who behaves in an ethical manner you wouldn't expect any less would you?
Forget it and move to BCG.
I'm not a lawyer either by the way, but a HH.