  We provide a general framework to describe cooling of a micromechanical
oscillator to its quantum ground state by means of radiation-pressure coupling
with a driven optical cavity. We apply it to two experimentally realized
schemes, back-action cooling via a detuned cavity and cold-damping
quantum-feedback cooling, and we determine the ultimate quantum limits of both
schemes for the full parameter range of a stable cavity. While both allow to
reach the oscillator's quantum ground state, we find that back-action cooling
is more efficient in the good cavity limit, i.e. when the cavity bandwidth is
smaller than the mechanical frequency, while cold damping is more suitable for
the bad cavity limit. The results of previous treatments are recovered as
limiting cases of specific parameter regimes.
