This is an exploration of Legendre spectral finite-element (LSFE) formulations for Reissner-Mindlin plates. The goal was to compare high-order LSFEs with standard low-order finite elements in terms of computational efficiency, and determine an optimal formulation for thin-walled elastic media. Simulations using various LSFE and standard FE formulations were carried out. Model performance is compared by examining the error as a function of both model size (DoF) and model efficiency (FLOPs) for the various formulations. Results showed that LSFEs using a mixed formulation consisting of nodal Gauss-Lobatto-Legendre quadrature for the bending matrix, and reduced Gauss-Legendre quadrature for the shear matrix were most computationally efficient of all elements tested.