I know the OP has decided where to stay, and I, too, LOVE both resorts. I just want to reply to this comment (and I know many people have posted similar concerns):
"We have not done the BC CL but we have stayed at the BC and it is a great location. I hear the lounge is very small and often so packed you cannot get in".
Just to put people at ease about staying at BC Club Level. We were there for a week in March when it was definitely pretty busy with Spring Breakers. I was worried about the lounge being too small, but I found that not to be true at all. We never had a problem getting in and getting food and drinks of all kinds. Occasionally most of the tables were taken, but the staff (who were ALL so wonderful) would be circulating and clearing things immediately and seeing if they could get us anything. Most of the time we were just grabbing stuff to go anyway. They have trays that you can use to bring stuff back to your room if you wanted. We had a full balcony so my husband and I would take our drinks back to our rooms. We found all the guests to be very considerate of one another. I cannot say enough nice things about the club level at Beach Club.
I wish I were going back right now and had to make the decision between BC and AKL!