Heavy-quark observables in ultrarelativistic heavy-ion collisions, like the nuclear modification factor and the elliptic flow, give insight into the mechanisms of high-momentum suppression and low-momentum thermalization of heavy quarks. Here, we present a global study of these two observables within a coupled approach of the heavy-quark propagation in a realistic fluid dynamical medium, MC@sHQ+EPOS2, and compare to experimental data from RHIC and LHC experiments. The heavy quarks scatter elastically and inelastically with the quasiparticles of the quark-gluon plasma (QGP), which are represented consistently with the underlying equation of state. We examine two scenarios: first, we interpret the lattice QCD equation of state as a sum of partonic and hadronic contributions, and second, as a gas of massive partonic quasiparticles. It is observed that independent of their momentum the energy loss of heavy quarks depends strongly on how the lattice QCD equation of state is translated into degrees of freedom of the QGP.