Active Debris removal using robotic manipulators onboard satellites is a promising way of cleaning up the space junk. However, complexities and non-linearities associated with the control of such coupled space-based systems present difficulties in their feasible implementation. Lack of a fixed base arises serious problems in controlling the space manipulators for precision tasks like capture of an orbiting space debris. This paper presents systematic modelling and control approaches for Rotation floating space robots in order to draw a comparison between them while tracking a moving target representing autonomous debris capture. We propose a Nonlinear Model Predictive Controller (NMPC) for the space robot in order to design an optimal path that the end-effector can follow while being controlled to capture the target. To the best of the knowledge of the authors, such a controller has not been tested for a Rotation floating space robot before. Further, the current work implements and reviews one of the most commonly used Transpose Jacobian Cartesian (TJC) controller for Rotation floating space robots through the use of Generalized Jacobian Matrix (GJM). The results provide sufficient evidence of the superior performance of the nonlinear model predictive controller over the TJC controller. Finally, the current work also implements the same nonlinear model predictive controller on a more popular state of the art Free floating space robot and compares it with the Rotation floating space robot.