What are the differences between McKinsey, BCG and Bain case interview style?

Bain and BCG will follow a traditional interviewee-led case, where you will need to present a framework and drive it to completion; BCG will further differentiate by often/typically/always denying a minute to gather your thoughts before the final conclusion

McK on the other hand is interviewer-led: you need to build a framework, but the interviewer will guide you and tell you what you should focus on. Slightly different, but if you can do the former well, the latter shouldn't be an issue.

PS: Many admits to one of MBB also get offers from the other two => skills are portable, if you know how to ace a case, you know how to ace a case