MM IB or MBB Consulting => BB/EB IB

Would it be easier to start out at a lower end (but well known) MM IB or an MBB Consulting firm if your goal is to move up to BB/EB IB after 2-3 years as an analyst?

Assumptions:

BB/EB is desired starting point but not a possibility whereas MM IB and MBB are both highly plausible.

Top 20 MBA can be plugged into the timeline to ease transitions (not meant to be an equalizer; would still like to know whether the MM or MBB would allow an easier move with or without the MBA).

Thanks in advance for your opinions.