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We study how heavy quark dynamics is affected by the nature of the bulk evolution of the QCD matter, the initial condition of the system, and the treatment of elementary interactions between heavy quarks and the surrounding medium. For the same initial condition and the same QGP expansion scenario we discuss the consequences of the assumption of a local equilibrium by comparing the consequences for the nuclear modification factor and the elliptic flows of charm quarks. For this purpose we employ the parton-hadron-string dynamics (PHSD), which is an off-shell microscopic transport approach, as well as the linearized-Boltzmann (LB) scheme obtained by coarse graining the PHSD bulk and assuming local equilibrium for the interactions of the charm quarks with the bulk. The $R_{\rm AA}$ of charm quarks stemming from the later LB approach is also compared to a genuine fluid dynamics evolution initiated by the coarse grained PHSD, which allows to further assess the consequences of reducing the full n-body dynamics. We then proceed to a systematic comparison of PHSD with MC@HQ, another transport model for heavy flavors which also relies on LB approach. In particular, we investigate the consequences for the nuclear modification factor of charm quarks if we vary separately the initial heavy quark distribution function in matter, the expansion dynamics of the QGP and the elementary interactions of heavy quarks of these models. We find that the results for both models vary significantly depending on the details of the calculation. However, both models achieve very similar predictions for key heavy quark observables for certain combinations of initial condition, bulk evolution and interactions. We conclude that this ambiguity limits our ability to determine the different properties of the system based on the current set of observables.