Data collection and analysis strategies have been developed for efficient and reliable crystallographic texture measurements at two recently upgraded neutron diffractometers: the Wide Angle Neutron Diffractometer Squared (WAND2) and the High Intensity Diffractometer for Residual Stress Analysis (HIDRA) at the High Flux Isotope Reactor located at Oak Ridge National Laboratory. These methods are demonstrated using measurements on a variety of textured samples, including multi-phase steel composites and polycrystalline calcite (CaCO3). Reference measurements were also made at VULCAN, the engineering diffractometer located at the Spallation Neutron Source. The texture data obtained on the different instruments are in agreement, and WAND2 is more time efficient than HIDRA. Two analysis methods were investigated, single-peak fitting to obtain individual pole figures for inversion and Rietveld texture analysis using MAUD. The impact of the differences between the various textures obtained was evaluated through the calculation of diffraction elastic constants, which is one application of the texture data collected. Both instruments were found to provide texture data that are suitable for complementing other analyses, such as residual stress mapping.