The autonomous manipulation of deformable slender structures by robots is a challenging task due to the infinite configuration space and non-linear mechanical behaviour of such objects. This work addresses the control of a robotic arm that grasps one end of a flexible rod, deforming it to achieve a desired shape. To tackle this highly underactuated problem, we designed a control scheme where the feedback from a camera is used to continuously update a Jacobian relating robot motions to object deformations. In this work, two approaches are considered to find an appropriate numerical representation for the shape: (i) the traditional position-based method, commonly used in the literature, which relies only on the position of feature points, and (ii) a novel SE(3)-based method which relies on features frames as elements of SE(3). The SE(3)-based method benefits from favorable theoretical properties, such as the invariance of the Jacobian with respect to rigid body motions. However, due to the nonlinear nature of the problem, the performance improvements in practical scenarios can hardly be predicted on a purely theoretical basis. Considering the high number of setup parameters, such as object length, feature positions, and their number, a purely experimental investigation is impractical. In this work, we present a simulation-based assessment procedure enabling a quantitative comparison between different control laws based on statistically relevant data across diverse configurations. While several simulation tools are available in the literature, we selected here a 2D simulator which outputs the static equilibrium configuration of the object for any given pose of the robot gripper. The computing time is very short as the solver only requires a minimization of the bending energy. This simulation-based method allowed us to run a large number of virtual experiments in parallel using computer clusters. After this extensive simulation campaign, the experimental validation on a real setup could be limited to a small number of specific, representative cases.