I've not played BAM, but I've used the other two. Competition is very good IMO. I used it exclusively for some time. I think it has good feel for a poly at the right tension. I also liked that it could be played until it broke most of the time without getting out of control. It's definitely a control oriented string.
PLII is similar to competition, but I found the feel to be a little more stiff, and it didn't seem to play quite as consistent. I found this a little odd, because it's supposed to be the successor to Competition. Spiky Shark is my new standard string, and I understand it's the same formulation as PLII, but it seems more consistent like Competition to me.