I actually view PhD/JD/MD candidates as the perfect applicants: You are smart, driven, typically highly quantitative, yet do not take the case for granted and are ready to learn.
I have both a Masters in Management and an MBA but wasn't better prepared to MBB than any one of you. Yes I thought I could prepare alone, and crashed on 3 separate occasions before finally hiring help my last (and ultimately successful) application.
To answer your question more specifically, I expect you to:
1. perhaps suffer a little more through some of the business concepts. You can get around this easily by reading the economist or WSJ for a few weeks and looking up foreign concepts
2. be better in math / statistics
3. above all, know how to develop a hypothesis and actually know how to prove/disprove it.
4. related to (3), know the difference between a hypothesis and its proof.
(3) and (4) should put you in the top quartile of the interviewees, right off the bat. You got this! good luck...