First round: very standard. Two fit questions, then a case interview, then "what questions do you have for me?" Interviewers are project managers, and have typically been at BCG for 3-5 years.
They have a standard quick turnaround. I interviewed twice (2017 and 2018) both times on a Friday. The first time they let me know I passed on Tuesday evening, the second time they let me know I passed Monday afternoon.
Second round: this round the interviewers are partners and the questions are a lot more open-ended. In the Seattle and Chicago offices, second round also involves a written case, where you get 45 minutes before the interview starts to go through a slide deck and solve a case with that data, which you then present to the interviewer.
In Seattle 2017, there was a written case with a friendly interviewer, then a regular case interview with a (deliberately) grumpy interviewer. I think they want to see how you respond to unfriendly clients. The written case was hard for me to organize - I don't know how much of that was the case and how much of that was just my nerves. Didn't pass.
In Chicago 2018, I had a regular case interview first. She asked fit questions, but they were more in the context of a conversation than specific fit questions. The case interview for that case was surprisingly open-ended and pretty difficult - she didn't have most of the information I asked for, and when I was clearly stuck she asked me to just wrap it up. It wasn't the worst I could have done, but I knew I had to really own the second case to get an offer.
This time, the written case was a lot easier to organize. I highly recommend reading the section in Victor Cheng's book on presentation interviews, as this gave me a strategy going in. I started the section with the interviewer by presenting my synthesis like I had just done a normal case, then the interviewer asked a few questions about how I got the numbers I did, asked if there were other things we could look at, etc. It was about the conversation and testing to see whether I could back up the claims and recommendations I'd made. Then he followed that up with several fit questions - again, more like a conversation than set fit questions. I definitely owned this case and I think I redeemed myself, because in the end I got the offer!