Ion populations with large perpendicular temperature anisotropies in the magnetosheath can excite both the mirror and proton cyclotron anisotropy instabilities. We compare kinetic aspects of these two instabilities using two-dimensional hybrid simulations, expanding upon an earlier work using one-dimensional simulations. Three simulation runs are examined: one in which the proton cyclotron instability has a higher linear growth rate, the second in which the mirror instability grows more rapidly, and the third in which the linear growth rates are identical. The last two runs include a large density of isotropic He++ ions to suppress the cyclotron instability. We find that initial growth occurs in all three runs at approximately the frequencies, wavenumbers, and obliquities expected by linear theory. As the system evolves, the power in both instabilities shifts to longer wavelength modes, and the characteristic frequency of the proton cyclotron instability decreases. In the first two runs, the instability with the larger linear growth rate dominates the wave energy at saturation, and in the third, the two instabilities contribute about equally. The proton cyclotron instability is relatively more important to wave-particle energy exchange than the mirror instability; its importance to proton isotropization is generally greater than that suggested by its contribution to the total wave energy, and it is almost solely responsible for heating the helium ions. ¿ American Geophysical Union 1994