  We perform a systematic comparison of three different jet energy-loss
approaches. These include the Armesto-Salgado-Wiedemann scheme based on the
approach of Baier-Dokshitzer-Mueller-Peigne-Schiff and Zakharov (BDMPS-Z/ASW),
the Higher Twist approach (HT) and a scheme based on the approach of
Arnold-Moore-Yaffe (AMY). In this comparison, an identical medium evolution
will be utilized for all three approaches: not only does this entail the use of
the same realistic three-dimensional relativistic fluid dynamics (RFD)
simulation, but also includes the use of identical initial parton-distribution
functions and final fragmentation functions. We are, thus, in a unique
position, not only to isolate fundamental differences between the various
approaches, but also to make rigorous calculations for different experimental
measurements using "state of the art" components. All three approaches are
reduced to a version which contains only one free tunable parameter, this is
then related to the well known transport parameter $\hat{q}$. We find that the
parameters of all three calculations can be adjusted to provide a good
description of inclusive data on $R_{AA}$ versus transverse momentum. However,
we do observe slight differences in their predictions for the centrality and
azimuthal angular dependence of $R_{AA}$ vs. $p_T$. We also note that the value
of the transport coefficient $\hat{q}$ in the three approaches to describe the
data differs significantly.
