Parallel Continuum Robots (PCR) have received a lot of attention in recent years. This paper presents a new 6-degrees-of-freedom PCR derived from the conventional 3-PPSR parallel manipulator. This robot is driven by three limbs consisting of two flexible rods each and replacing the spherical and revolute joints of the original version. Each limb is mounted onto two linear axes arranged in series. To allow a direct comparison between the articulated and the continuum version, the parallel mechanism of an industrial manipulator has been replaced by an elastic structure of the same size. The simulations and the experiments show that the flexible counterpart of the manipulator is able to achieve a larger workspace, increasing the range of motion by 150% for rotations and by 157% in elevation. Moreover, the position repeatability is improved by 47% (reaching 3.4 µm) and the orientation repeatability by 57% (reaching 14.3 µrad). This can be explained by the removal of the spherical and revolute joints but also by the constant stress in the structure that acts as an anti backlash system on leadscrew actuators.