Sidi's answer covers most of the key points very well. I would add a couple more points on how interviews with partners can differ from interviewers with more junior team members:
1) Partners are more likely to have their own cases or "go rogue" and ask very out of the box questions. So be ready for potentially surprising/out of the box case interviews
2) Partners also have more freedom on the behavioural questions. I was once asked the standard "where do you want to be in 10 years" but the partner really wanted to focus on my personal life aspirations - e.g. why or why not having kids. It was an odd interview but he was definitely trying to determine how I thought and how sincere I was in my responses.
3) As Sidi mentioned, if there was a point that was mentioned as a weakness in a previous interview, they are also likely to really push you on that area (e.g. if your feedback was that you were a bit indecisive, they might put you on the spot and force you to make decisions/recommendations even in uncomfortable situations).