In this work, we study efficient methods based on sparse grids and generalized Polynomial Chaos Expansion (gPCE) to address the curse of dimensionality in UQ problems. We compare methods that compute quantities of interest (QoIs) directly from moment approximations with those that construct gPCE surrogates and extract QoIs from the expansion coefficients. In addition, we discuss the impact of spatial adaptivity using dimension-wise refinement, and compare it with traditional Gaussian quadrature-based methods. The results suggest that spatial adaptivity will normally improve accuracy. However, if we use adaptivity to compute PC coefficients, then errors due to internal aliasing, especially with low order quadrature like the trapezoidal rule, will limit the benefit gained from using adaptivity.