We analyze the dust emission features seen in Spitzer Space Telescope Infrared Spectrograph (IRS) spectra of red supergiant (RSG) and oxygen-rich asymptotic giant branch (AGB) stars in the Large Magellanic Cloud and Small Magellanic Cloud galaxies and in various Milky Way globular clusters. The spectra come from the Spitzer Legacy program SAGE-Spectroscopy (PI: F. Kemper), the Spitzer program SMC-Spec (PI: G. Sloan), and other archival Spitzer-IRS programs. The broad 10 and 20 micron emission features attributed to amorphous dust of silicate composition seen in the spectra show evidence for systematic differences in the centroid of both emission features between O-rich AGB and RSG populations. Radiative transfer modeling using the GRAMS grid of models of AGB and RSG stars suggests that the centroid differences are due to differences in dust properties. We investigate differences in dust composition, size, shape, etc that might be responsible for these spectral differences. We explore how these differences may arise from the different circumstellar environments around RSG and O-rich AGB stars and assess effects of varying metallicity (LMC versus SMC versus Milky Way globular cluster) and other properties (mass-loss rate, luminosity, etc.) on the dust originating from these stars. BAS acknowledges funding from NASA ADAP grant NNX13AD54G.