With tongue firmly planted in cheek:
McKinsey: like being a priest in some Jesuit order or Opus Dei. Culture is austere, fascist (authoritarian), and patronizing/arrogant. Some of the personalities (*ahem* sociopaths) in this firm are so intense that they can come across as creepy and predatory. But, they relish in the notion of some "fraternal order or code of McK alums" like some sort of secret society -- but not without their form of mortification (their internal review system is the consulting version of priests punishing themselves; it's brutal but they embrace it like only a good masochist would). In Star Trek terms, they would be the Klingons and Romulans.
Bain: if McKinsey is like some gothic church, Bain is a country club; a mix of genteel gentlemen and fraternity brothers who watch each other's back and have a good time doing it. In many respects the antithesis of McKinsey - it's small and tight knit, much more chummy and more "loosey goosey" in its culture. If McKinsey folks are confrontational (with each other, like warriors!) to a fault, because of Bain's more "chummy" culture, it can be harder to read people's true intentions. In Star Trek terms, they would be the humans -- Kirk, McCoy, Scotty, Sulu, Picard, Riker, LaForge.
BCG: closest to a university faculty or think tank. Collaborative, analytical, almost wonkishly analytical at times. Nerdiest of the three. But also the firm with the weakest cultural identity of the three - which may not always be a bad thing -- it's the least conformist as a result (i.e. with less of a strong culture, it can be less oppressive of a place to work; less pressure to have to "fit in" to some heavily defined cultural norm). In Star Trek terms they would be the Vulcans and androids - Spock, Data.
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