Don't worry about it too much. However, several things might be different:
1) I would expect a bit more structured and demanding approach to the fit part. The partners are more experienced and they will challenge every single detail of your story. So make sure that you have a couple of backup stories.
2) As for the cases - Partners and Directors (and some APs) have their own favorite cases and may want you to lead the case. The key difference: You lead the case through the structure you've prepared a) asking questions and trying to identify the root-cause of the problem in the branch of your structure b) making a transition to the next branch c) proactively calculating the data and making data-driven conclusion from the data they give you d) Making a conclusion when they ask you to finish a case
It may seem to you that these 2 types of cases are different, however, the interviewer-led type is just a simplified version of the interviewee-led case. My advice is to always prepare in the interviewee-led format so that you could solve both easily.