I'd always heard "Big Six" referring to the (brief) post-Castellamarese period where the Schultz group was the last Jewish organization standing. (i.e., the five families and Schultz). Not so much a commission as much as a realistic grouping of the powers in the city.

I've read that book more than a few times. The bios on the old-timers are entertaining and written well, and that's about all it has going for it. It's really more of a product of a different age, I think, where "real" mob workings weren't as widely exposed as they are now, and any information was better than good information to a lot of the intended audience.