Personally I don't keep large, aggressive SA/CA cichlids with any of my bichirs. In my experience, cichlids have a tendency to get territorial (especially when it is time to start preparing a nursery) and bichirs don't seem to have much concept of another fish having a territory so they simply wander wherever they feel like going and occasionally get beaten up by the cichlids. In general, the same goes for most of the Rift Lake cichlids as well (and even the larger African riverine species).
-Joe