Airfoil shape optimization is imperative for enhancing the aerodynamic performance of the aircraft. In the shape optimization process, geometry parameterization holds a pivotal role; directly influencing its robustness and efficiency. In this study, Adjoint-based shape optimization of the airfoil RAE-2822 was performed at transonic Mach while employing two parameterization methods – Hicks-Henne and FFD. The prime objective is to compare the efficiency of parameterization techniques and form comparison metrics based on their five fundamental characteristics - Parsimony, Intuitiveness, Orthogonality, Completeness, and Flawlessness. The optimization framework is composed of an open-source CFD solver, a discrete adjoint solver for gradient evaluation, and a gradient-based optimizer (SLSQP) for optimization. While using both techniques, the process resulted in a total drag reduction of around sixty-seven percent and an increase in aerodynamic efficiency by nearly three times. However, in the comparison metrics, it was seen that FFD outperforms Hicks-Henne exhibiting better properties in terms of parsimony and intuitiveness.