  The Baryon Acoustic Oscillations (BAOs) or baryon wiggles which are present
in the galaxy power spectrum at scales 100-150Mpc/h are powerful features with
which to constrain cosmology. The potential of these probes is such that these
are now included as primary science goals in the planning of several future
galaxy surveys. However, there is not a uniquely defined BAO Method in the
literature but a range of implementations. We study the assumptions and
cosmological performances of three different BAO methods: the full Fourier
space power spectrum [P(k)], the `wiggles only' in Fourier space and the
spherical harmonics power spectrum [C(l)]. We contrast the power of each method
to constrain cosmology for two fiducial surveys taken from the Dark Energy Task
Force (DETF) report and equivalent to future ground and space based
spectroscopic surveys. We find that, depending on the assumptions used, the
dark energy Figure of Merit (FoM) can change by up to a factor of 35 for a
given fiducial model and survey. We compare our results with the DETF
implementation and, discuss the robustness of each probe, by quantifying the
dependence of the FoM with the wavenumber range. The more information used by a
method, the higher its statistical performance, but the higher its sensitivity
to systematics and implementations details.
