IMO, the only system I don't like is Suzuki. I had a beginning sax student that had been taught using that method and I thought he was pretty decent -- until one day I handed him an arrangement of "Twinkle Twinkle Little Star" or some such to play with him as a duet and he wasn't playing the right notes.
He couldn't read the music, nor did he know what fingerings corresponded to what notes. He WAS able to listen to me play a phrase and duplicate it, which is commendable, but when I say, "Finger a D" and you say, "What?" there's a problem.