In real life problems uncertainties, for instance through uncertain boundary conditions or manufacturing imperfections, may affect the performance of an aerodynamic shape significantly. In order to measure the impact of uncertainties on the performance of an aerodynamic shape, statistical moments (usually the mean value and variance) of the Quantity of Interest (QoI, e.g. the lift or drag forces) have to be quantified through Uncertainty Quantification (UQ) techniques. This paper compares a number of variants of the Method of Moments (MoM) and the non-intrusive polynomial chaos (niPCE) approaches to UQ. Regarding the MoM, firstand second-order derivatives of the QoI with respect to the uncertain variables are necessary for formulating its first-(FOSM) and second-order (SOSM) variants, respectively. These are computed using a combination of continuous adjoint and direct differentiation of the governing (flow) equations. The statistical moments of the QoI can, then, easily be computed in terms of the QoI value and derivatives computed at the mean values of the uncertain variables. The results of the above-mentioned MoM variants are additionally compared to a number of niPCE variants developed and utilized by the authors in the past. The UQ variants of MoM and niPCE are then compared in terms of cost and accuracy of the computed statistical moments of the QoI. Comparisons also include results of the Monte Carlo method which acts as the reference method. The two benchmark cases used for the comparison include an airfoil under uncertain flow conditions and fluid properties as well as the DrivAer car model, under uncertain flow conditions.