Flexible medical instruments, such as Continuum Dexterous Manipulators (CDM), constitute an important class of tools for minimally invasive surgery. Accurate CDM shape reconstruction during surgery is of great importance, yet a challenging task. Fiber Bragg grating (FBG) sensors have demonstrated great potential in shape sensing and consequently tip position estimation of CDMs. However, due to the limited number of sensing locations, these sensors can only accurately recover basic shapes, and become unreliable in the presence of obstacles or many inflection points such as s-bends. Optical Frequency Domain Reflectometry (OFDR), on the other hand, can achieve much higher spatial resolution, and can therefore accurately reconstruct more complex shapes. Additionally, Random Optical Gratings by Ultraviolet laser Exposure (ROGUEs) can be written in the fibers to increase signal to noise ratio of the sensors. In this comparison study, the tip position error is used as a metric to compare both FBG and OFDR shape reconstructions for a 35 mm long CDM developed for orthopedic surgeries, using a pair of stereo cameras as ground truth. Three sets of experiments were conducted to measure the accuracy of each technique in various surgical scenarios. The tip position error for the OFDR (and FBG) technique was found to be 0.32 (0.83) mm in free-bending environment, 0.41 (0.80) mm when interacting with obstacles, and 0.45 (2.27) mm in s-bending. Moreover, the maximum tip position error remains sub-millimeter for the OFDR reconstruction, while it reaches 3.40 mm for FBG reconstruction. These results propose a cost-effective, robust and more accurate alternative to FBG sensors for reconstructing complex CDM shapes.