Schweizer2,
It can depend on where you're booking from. Where I live (in The Netherlands) the KLM site tends to offer cheaper fares with AF than KL simply because it involves a connection in Paris. However, if I book KL from either BRU or DUS (via AMS) I can get equally good bargains. Since I live closer (by road) to both BRU and DUS than AMS that suits me nicely. Same as a poster above, I avoid AF like the plague, even if it costs me more to do so.