In this work, the authors investigate the behaviors of the two main classes of pansharpening methods: those based on component substitution (CS) or spectral methods and those based on multiresolution analysis (MRA) or spatial methods, in the presence of temporal and/or instrumental misalignments between the multispectral (MS) and panchromatic (Pan) data sets, that is, whenever MS and Pan are not jointly acquired at the same time and/or from the same platform. Starting from the mathematical formulation of CS and MRA pansharpening and from the spectral model between the Pan and MS channels, estimated through the multivariate linear regression between MS and spatially degraded Pan, it is proven that both CS and MRA methods may lose geometric sharpness in the case of a spectral mismatch, but spatial methods preserve the spectral diversity of the original MS data set regardless of the date or instrument of Pan image acquisition. Conversely, spectral methods also suffer from a loss of spectral fidelity to the original MS data set that is inversely related to the success of the spectral match between MS and Pan, measured by the coefficient of determination of the multivariate regression. An experimental setup exploiting GeoEye-1 and QuickBird data sets demonstrates the validity and intrinsic limitations of the proposed theoretical models. Depending of the target application, one class of methods may be preferred to another: Whenever spectral fidelity of pansharpened products to the original MS data sets is crucial, spectral methods should be avoided, and spatial methods are to be preferred.