Impossible to judge recorded sound through your own system but what I do can pick up is that the JBL seems to be better for TV which makes sense. It is less airy and the voices are coming more from center whereas with the Edifier the sounds sounds more enveloping which would make it my pick for music. Again, not talking about the color of the sound, just the feel on how the mic is seemingly to pick up the direction of the sound
Having the soundbar in front of the edifier speakers isn't good for sound. You should placed the soundbar on top of sattelites and that would been better for both systems.