A few things:
1) It seems you have already made up your mind about Strategy& Middle East
2) You make some very very large generalisations, which make me think you've jumped to conclusions (I suspect confirmation bias pre point #1)
3) There are 8 Strategy& offices in the ME. They will be different. Furthermore, each practice will be different, and each Partner will be different. You need to appreciate the nuance here. It's imppossible that "Everyone there is from AUB"
4) The best way to find out? Meeting some of the people in the offices you're interested in!
Outcome 1: You get a gut feeling (or concious view) that it's not the right office and you move on.
Outcome 2: You realize you like the office, and now you have a contact that might be able to refer you. Win-Win!
5) Finally, not sure what you're asking in your last paragraph? Is it why Booz fell from the ranks? Simply, it would be due to the acquisition + name change. A lot of top brass left and their way of doing things was changed....as happens in many acquisitions.