People aren't talking about any 2 sites in particular, it's simply that you get to do a couple dives in the area that many or most folks consider the best diving in Belize. The long haul is getting out there. Once you are out there, there's multiple sites along those walls - the liveaboards stay there most or all of the week. The specific sites chosen may have to do with the dive ops routine, conditions, or if someone else is already on a mooring - but not whether they are coming from AC or CC.
I wouldn't worry too much about what specific sites they might dive, but more on finding an op that will do the trip, that you feel good about doing the Blue Hole with, and that has a comfortable boat for the long ride/day you'll be spending on it.