Magnetosheath plasmas are typically characterized by a proton &bgr;>1 and a proton temperature anisotropy T⊥/T∥>1. Such plasma is unstable to both the ion cyclotron anisotropy and mirror instabilities, and evidence for both of these growing modes has been found in the magnetosheath. In this paper, we use one-dimensional hybrid simulations to investigate the kinetic properties of these two instabilities. We find that, for moderate values of ion &bgr; and temperature anisotropy, the two instabilities produce similar levels of turbulence, but that the cyclotron instability apparently produces higher flucturation levels than the mirror instability for high &bgr; or anisotropy. Although both instabilities saturate by reducing the ion temperature anisotropy, mirror waves accomplish this through the use of the wave magnetic fields, whereas cyclotron waves do so by using the wave electric fields in resonant interactions with the ions. Consequently, mirror waves preferentially affect those ions with large magnetic moment, while cyclotron waves affect a broader range of ions and thereby domiant the isotropization process even when the mirror mode in somewhat stronger. We also investigate the utility of transport ratios as mode identifiers, and find that the Alfv¿n ratio in particular can be useful in distinguishing between the two modes. ¿American Geophysical Union 1992