CFA is specific and universally recognised certification. Whether you study for it taking classes in Manhattan or over a radio broadcast in Siberia, it's the same thing.
An MBA, as a certification, is one of the most misunderstood ones. There's a HUGE difference in having one from a top 10 business school at a global level, a top 10 school in a major western economy, a top 10 school in a lesser economy.
I'm not sure where you want to try and apply for jobs in consulting. If it's in Germany, an MBA from a renowned German university could be seen better than a CFA certification, because that's more tied to the anglosaxon world I reckon.
Also, are you sure want to do strategy consulting? Do you have clear idea of what you'll be doing day to day? Do you understand that it somehow close to academic/industry research at times?
Have you considered operational implementation consulting work in the primary and secondary sector?