To be honest, they don't differ much. And both people from McK and BCG know this, so it's not like they're going to phrase the question the way you did.
What I'd recommend you do instead is to read in detail the description on BCG's website and then try to use the reasons they provide there. Basically, play back what they communicate outwardly.
Additionally, it always helps if you know somebody who works there. Have a conversation with them to get their perspective and also mention in the interview that you knowledge is informed by having spoken with one of their employees (that always makes the answer seem more genuine).
If you don't know anybody, then I'd recommend you read this ARTICLE I wrote about how to network with consultants through coffee chats to learn more about the firms and get referrals.