First-principles Raman spectra have been computed for several new vaterite structural models that have been recently proposed, and compared with spectra recorded on a set of biogenic, geological and synthetic samples. This set includes new measurements collected on Herdamania momus spicules (Great Barrier Reef, Queensland, Australia), which are known to have purity and crystallinity that are higher than for other biogenic samples. Overall, due to the close structural connection between the various models, the computed Raman spectra are found to be broadly similar. However, the spectra obtained for the two most stable models (monoclinic C2 and trigonal P3221, corresponding to two different polytypes of vaterite) exhibit features that are in excellent agreement with the experimental spectra, whereas the other theoretical structures show minor peaks that are not observed experimentally. When comparing the spectra for the two lowest energy structural models (C2 and P3221), the differences are too small to discriminate between these candidates. The Raman spectrum of H. momus is of higher quality with respect to spectra obtained in previous studies on other biogenic samples. However, there is no significant and systematic difference with respect to samples of geological and synthetic origin. (Graph Presented).