just had my 2nd alumni interview. i was lucky in that both interviews were super conversational and low pressure. it was a bit like talking to a mutual acquaintance you just met, sharing your life stories, interests, and goals. it flowed naturally from question to question (work experience, future goals, why mba, etc.) and would include their own stories and thoughts. the first alumni interviewer said the point of the interview for him was to answer the question "would i want this person to be my classmate?". basically, to gauge fit.
they didn't ask me any behavioral questions ("tell me about a time when...") which was surprising.
two things i noticed. one is both were EE undergrads, same as me. i think INSEAD pairs people with same backgrounds so if you're a consultant, be prepared to interview with a consultant who might ask completely different types of questions (maybe case studies? i dunno).
second is both interviewers tried to gauge my interest in INSEAD. both asked if i was applying to other programs. since i'm american, both asked why i wanted to do the 1 year European mba vs the standard US 2 year. both ask why INSEAD considering it has relatively lower brand equity in US. both asked which campus i wanted to be at. sounds like they wanted to know if INSEAD was my first choice or an after thought. i think similar to Tuck (and i guess everywhere), INSEAD wants to know that you will accept their offer if they give you one and that they aren't a backup school to S/H/W.
overall, i compare it to having a casual, mature, intelligent conversation with a very interesting person in your industry. in fact, i would not have minded if we continued the conversation longer.