I disagree with the fact that those two type of cases are very different, and I think it makes so many people loose focus on what really matters.
I am happy you ask this, since I have seen quite some posts in the Q&A lately regarding this topic, and I have quite a strong opinion.
I have seen so many candidates in the past putting such focus on trying to conduct a case in an interviewer vs. interviewee lead way (or vice-versa) in the past, that they get their eyes off the ball and what really matters here.
Think it this way, because it´s really this simple: you will be confronted with a business problem and someone with quite an experience in solving those would evaluate the way you think, structure and problem-solve. Hence, just focus on that: an impressive solution and process.
Hope it helps!