I'm about to finish my Ph.D. so I can give you my view of it.
Both options present their own set of Pros/Cons that you should take into account:
1) Go straight away for MBB:
Pros: Starting early in consulting, MBB may fund your further education, seeing if you really enjoy it, etc.
Cons: A PhD is usually from 3 to 5 years so if you're in MBB maybe you don't want to stop that for 5 years to do something unrelated that won't help you that much (especially if not related to Eng., Manage. or Finances in any way)
2) Doing PhD first:
Pros: You just finished your masters so it's easier to follow your academic and start the PhD right away; Gaining advanced degree could allow you to move straight away to a more advanced position once you apply for consulting.
Cons: Sometimes with a PhD you will be seen as not having any real work experience and too old to start from an entry-level. Some firms/geographies don't care for PhD.
Overall: like everything in life, there is more than one way to accomplish something. As long as you are willing to put in the time and adjust to the circumstances facing your path you can accomplish anything you put your mind into.