Off-line robot dynamic identification methods use the Inverse Dynamic Identification Model (IDIM), which calculates the motor torques that are linear in relation to the dynamic parameters of both links and drive chains, and use linear least squares technique (IDIM-LS technique). For most robots, the only available data are the motor position and the motor torques which are calculated as the product of the known current reference signal by the joint drive gains. Then the accuracy of links parameters may be limited by noise and error modeling in the drive chains. The Kuka LWR robot (industrial version IIWA: Intelligent Industrial Work Assistant) gives the possibility for an industrial robot to investigate this problem using the joint torque sensors data, measured at the output of the harmonic drive geared drive chains, to identify only the links inertial parameters without the errors coming from the drive chains. This paper focuses on the comparison of the accuracy of the identification of the dynamic parameters of the rigid model of the LWR4+ version, which is very popular in robotics research, using measures of the motor positions and the motor currents, or the torque sensors measurements or both side data. This paper is giving a first complete and reliable identified rigid dynamic model of the LWR4+, publicly available for the robotics community. Moreover, this work shows for the first time the strong result that motor torques calculated from motor currents can identify the links inertial parameters with the same accuracy than using joint torque sensors at the output of the joint drive chains.