I applied for McKinsey through the university career site. They responded to me fairly quickly with an offer for a first-round interview, which consisted of 2 45-minute long interviews and a written test. The written test was awful, but it must not have mattered very much. It's still unclear to me what they were trying to get at with it. If you have to take one, I would use the one on their website as practice to know what to expect, but don't put too much pressure on yourself for it.
Unlike BCG, McKinsey cases are very straightforward--at least, for first round. There were fairly obvious questions and answers in my case. The interviewers picked one thing off my resume for the fit part of the interview and really delved deep into it, probing for my thought process in a particular example story I told (I assume it's also to make sure I'm not fabricating the story in any way).
Second round was in the office and had three interviews. The office is great and the recruiters are very nice. I also like that they give you bios of interviewers so you know their background. The cases this time were less obvious, more vague, and I think they were really looking for though process and making sure you are able to consider a variety of factors, rather than your ability to solve a straightforward problem. The fit part was like the last one--very specific, very detailed. My interviewers were all incredibly friendly and I loved the atmosphere there. It was professional and also felt very cohesive.
My advice would be to have stories in mind for difficulties in anything you list on your resume, and also to really engage the interviewers in a conversation, rather than just giving them a spiel.