I disagree with the other experts here. Second round interviews at Bain are not inherintly more difficult than 1st round interviews. However, they are often a bit less structured. Assume that a senior partner has given houndreds of interviews. At one point, people usually stop applying a strict structure to the case and come in with printed hand-outs that they will give you.
Interviews with very senior consultants are often more of an interlectual conversation around the case, rather than the very fomalized structure junior interviewers apply. But that must not fool you: You should apply the same way of structuring your way through the case and always make sure to communicate in a very structured and pointed way, even if the interviewer pushes the conversation more into a brainstorming, rather than a typical case interview.