In the legal sector, the branding you want to have is the one other parties fear going up against. Therefore, they might tend to settle rather than going to trial which is not only expensive but that they probably also suspect they might not win.
So, given that understanding of powerful brands in law, the top four are:
Boies, Schiller & Flexner
Kirkland & Ellis
They got that brand identity thanks to the latest survey by BTI Consulting Group. It had interviewed plenty of inhouse counsel about what law firm they didn't want to encounter on the other side of a legal issue. Those four took the top slots. Those findings are here in the executive summary of the more general trend report BTI has published.
In addition to dealing from a position of strength, being this kind of brand also generates other wonderful stuff like extreme pride among the workforce. They go beyond. They are loyal, with a low level of leaks. That no organization can buy. In its heyday of being an experience economy player Sephora Cosmetics was also that kind of brand. Seasonal help carried the same aura as full time employees. They wore their uniforms the way Marines do.
Of course, the marketing communications staff at these four law firms can milk this for all it's worth - and that's plenty.