<p>Proper Generalized Decomposition (PGD) represents an important class of reduced order modeling approach for solving partial differential equations in terms of residual minimization among a selected number of modes, each in a variable-separated form. We explore mode selection within the PGD framework, contrasting it with the Singular Value Decomposition (SVD). They yield optimal rank-one series of the solution for residual minimization and error reduction, respectively. Taking an elliptic equation in two-space dimensions with a two-mode source term under certain constraint as an example, we analytically study the residual minimization and prove that the mode ordering in the optimal PGD rank-one series differs from that in SVD. With general source terms, numerical simulations for the elliptic equation, the heat equation and a parametrized parabolic equation verify and extend the theoretical results. In this way we reveal that the PGD algorithm does not provide optimal numerical convergence in general. We further discuss the preconditioning of PGD, utilizing exponential sum approximations for high-dimensional operators, which rectifies the residual functional and better aligns with SVD.</p>