I don’t know any detail about McK Digital but I have a fairly good view of what BCG Gamma is: I am a data scientist there.
BGC Gamma is a virtual office within BCG. We are not a back office, we are data scientists with strategy consulting skills (more people with MSc or PhD than MBA). We are fully involved in the client relationship, participate to client meetings, steering committees etc. Some cases are 100% Gamma but we often work jointly with BCG classic (mixed case teams).
We deliver custom data science-based solutions (machine learning, numerical optimization...) to our clients to allow them to take advantage of the huge impact data analytics and AI are having on the business world: pricing optimization, personalized marketing, more dynamic logistic, etc. We create the data science models, program the software (in Python or R essentially) and deliver working solutions, not only advices and slide decks. To build those solutions we need to understand both data science and business.
Our career progression is globally align with the rest of BCG. We actually have consultants from classic BCG transferring to Gamma. There is a partner track at Gamma.
I hope this helps.