Q: Which approach to the issue of career push inside MBB - MBA or one more PhD attempt - would you recommend?
You may not need an advanced degree to progress (although this also depends on the company and geography, so I would check within your firm).
Between the two, the MBA is going to be handier and probably shorter (INSEAD for example is just 1 year).
The main advantages of an advanced degree – in particular an MBA – are the following
- If you leave for the corporate world it may open more doors
- Assuming the MBA is a top one, it is a great way to build a strong network, in particular if your undergrad did not have a strong brand
- Although it may not be required for career advancement, the time spent for an MBA could be recognized by your consulting company for career progression, meaning you won't “waste” time by doing it (and get the pluses above)
Theoretically, an MBA is also going to provide knowledge, but the extra knowledge you will get probably won't compensate for the one lost in the 1-2 years you may get working.
Overall, if your future exits require an MBA (or PhD) or you want to leverage a stronger network, an MBA could definitely make sense, in particular if paid by the firm.