As a consulting firm that focuses on implementing technology to solve business/data centric problems we do not focus in a specific vertical market (HR or Legal). Instead we focus on specific types of problems and clients who need a specific range of advice. Over the years we have done a lot in many different industries but we now have 3-4 industries that we know a lot about.
I think you do need to focus on being "the best" at something, otherwise why would a prospective client choose you over another candidate?
Typically what happens is consulting companies either have a specific domain knowledge like "the problems faced by lawyers" or they simply end up with a good reputation in a given few industries ... this leads to them gaining more domain knowledge in that area ... thus more likely to be thought of by prospects in that industry.
... Most companies will focus on a few key areas so they don't confuse their most likely market or give their competitors the chance to say "we do YOUR thing better". That said nearly all of them will do things outside of their stated scope, they just don't push that through their central branding message.