Applied online with NY office as my third choice. Received invitation via e-mail a few weeks later to come to a 1st round interview in the Tel Aviv office on behalf of NY. I was living in a nearby country at the time, but they flew me out and put me up in a hotel (odd -- though nice -- for a 1st round).
1st round consisted of two one-on-one case interviews with BCG Project Leaders. Each interview began with a few motivation/personal questions (why BCG, why the NY office, walk me through key points in your resume, etc.). Interviews were difficult and the cases did not have obvious solutions. It's really important when trying to isolate the problem in the case to think holistically about the business at hand and how it works and its operating cycle, etc.
Eventually solved both cases (with some help from interviewers). Interviewers were very friendly and super helpful in answering my questions. Very positive experience.
Found out a week later that I did not pass to the final round. Feedback was that once I had set up structures/frameworks, I then strayed from actually using those structures to solve case. Also my suggestions were not very creative and I relied too much on the interviewer to drive the case's progress (probably a function of my having recently done McKinsey interviews which are interviewer led). Also, my motivation for consulting was a little too general and unspecific. Definitely have a clear connection ready to share for why consulting will help you meet your career goals.
Having interviewed with McK, Bain, and BCG, I think BCG's cases are the hardest and require the most creativity and "out of the box" thinking.