  We experimentally investigate the relative advantages of implementing
weak-value-based metrology versus standard methods. While the techniques
outlined herein apply more generally, we measure small optical beam deflections
both using a Sagnac interferometer with a monitored dark port (the
weak-value-based technique), and by focusing the entire beam to a split
detector (the standard technique). By introducing controlled external
transverse detector modulations and transverse beam deflection momentum
modulations, we quantify the mitigation of these sources in the
weak-value-based experiment versus the standard focusing experiment. The
experiments are compared using a combination of deterministic and stochastic
methods. In all cases, the weak-values technique performs the same or better
than the standard technique by up to two orders of magnitude in precision for
our parameters. We further measure the statistical efficiency of the
weak-values-based technique. By postselecting on $1\%$ of the photons, we
obtain $99\%$ of the available Fisher information of the beam deflection
parameter.
