  Fisher-matrix methods are widely used to predict how accurately parameters
can be estimated. Being computationally efficient, this approach is prompted by
the large number of signals simulated in forecast studies for future
gravitational-wave (GW) detectors, for which adequate analysis tools and
computational resources are still unavailable to the scientific community.
However, approximating the full likelihood function with a Gaussian may lead to
inaccuracies, which we investigate in this work. To assess the accuracy of the
Fisher approximation, we compare the results of the Fisher code GWFish against
real data from the Gravitational Wave Transient Catalogs (GWTCs) provided by
the Virgo/LIGO Bayesian analyses. Additionally, we present a sampling algorithm
to include priors in GWFish, not only to ensure a fair comparison between
GWFish results and the Virgo/LIGO posteriors but also to investigate the role
of prior information and to assess the need to include it in standard Fisher
analyses. We find that the impact of priors depends mostly on the level of
signal-dependent degeneracy of the waveform parameterization, and priors are
generally more important when the level of degeneracy is high. Our findings
imply that Fisher-matrix methods are a valid tool for ET science-case studies.
