A320 procedures for one thrust reverser inoperative; why is the old procedure more efficient?
Does the position of the controls for the second motor really influence the behaviour of the first one?


No, it influences the activation of various other systems like the autothrust, the airbrakes, as well as the thrust reversers.


  how it is more efficient?


Because in the new procedure the engine with non-functioning reverser starts to spool up before the system realizes the reverser did not deploy and cuts it again, so for a moment it produces forward thrust. The old procedure avoids this.