Our aim was to establish the capability of spatially resolved acoustic spectroscopy (SRAS) to map grain orientations and the anisotropy in stiffness at the sub-mm to micron scale by comparing the method with electron backscatter diffraction (EBSD) undertaken within a scanning electron microscope. In the former the grain orientations are deduced by measuring the spatial variation in elastic modulus; conversely, in EBSD the elastic anisotropy is deduced from direct measurements of the crystal orientations. The two test-cases comprise mapping the fusion zones for large TIG and MMA welds in thick power plant austenitic and ferritic steels respectively; these are technologically important because, among other things, elastic anisotropy can cause ultrasonic weld inspection methods to become inaccurate because it causes bending in the paths of sound waves. The spatial resolution of SRAS is not as good as that for EBSD (~100 μm versus ~a few nm), nor is the angular resolution (~1.5 degrees versus ~0.5 degrees). However the method can be applied to much larger areas (currently on the order of 300 mm square), is much faster (~5 times), is cheaper and easier to perform, and it could be undertaken on the manufacturing floor. Given these advantages, particularly to industrial users, and the on-going improvements to the method, SRAS has the potential to become a standard method for orientation mapping, particularly in cases where the elastic anisotropy is important over macroscopic/component length-scales.