So, if one had to generalize, what are the cultures of these firms? Be forewarned that these are not completely accurate, but rather one way of looking at things that are not necessarily true in every context.
McKinsey sells itself as a "team of leaders." They also have a huge public service bent, serving as a platform for budding politicians. McKinsey tends to hire charismatic, people-leaders who know how to sell anything and everything. A potential drawback at the firm is the level of toolishness, and the inclination to talk crap about the two the B's. They do think they are the gold standard of management consulting, given their strong brand. McK operates on a Monday through Thursday traveling model, where teams and consultants spend most of their time on ground at the client site. This makes for interesting and global travel.
Bain is the youngest of the top three firms, both in firm history and corporate culture. Others may call the firm fratty, as the bulk of hires each year tend to be recently minted college grads. The main drawback is the need to socialize and hang out with colleagues. Bain has made a huge rise as of late and is known for being incredibly entrepreneurial and innovative, creating affiliated organizations in specialized practice areas. Bain Capital, a private equity firm, and Bridgespan Group, a non-profit consulting arm, are two well-known and industry leader spinoffs from the firm. People are known to be extremely personable and the most well-balanced in terms if having a life outside of work.
Boston Consulting Group is an business practice innovator, with their consultants penning many of the frameworks used by all consulting firms in analyzing client data. As a result, BCG tends to have a more academic and intellectual bent than the other firms. BCG is all about the consultant, a post MBA position, though Associates (undegrad hires) are known for getting high-level responsibility almost tantamount to the consultant line of work. BCG is often called the high society of consulting, with a professional and proper attitude of its consultants in everything they do.