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Context. In the 2017 observation campaign, the Event Horizon Telescope (EHT) for the first time gathered enough data to image the shadow of the supermassive black hole (SMBH) in M 87. Most recently in 2022, the EHT has published the results for the SMBH at the Galactic Center, Sgr A*. In the vicinity of black holes, the influence of strong gravity, plasma physics, and emission processes govern the behavior of the system. Since observations such as those carried out by the EHT are not yet able to unambiguously constrain models for astrophysical and gravitational properties, it is imperative to explore the accretion models, particle distribution function, and description of the spacetime geometry. Our current understanding of these properties is often based on the assumption that the spacetime is well described by the Kerr solution to general relativity, combined with basic emission and accretion models. We explore alternative models for each property performing general relativistic magnetohydrodynamic (GRMHD) and general relativistic radiative transfer (GRRT) simulations. Aims. By choosing a Kerr solution to general relativity and a dilaton solution to Einstein-Maxwell-dilaton-axion gravity as exemplary black hole background spacetimes, we aim to investigate the influence of accretion and emission models on the ability to distinguish black holes in two theories of gravity. Methods. We carried out 3D GRMHD simulations of both black holes, matched at their innermost stable circular orbit, in two distinct accretion scenarios: standard and normal evolution (SANE) and a magnetically arrested disk (MAD). Using GRRT calculations, we modeled the thermal synchrotron emission and subsequently applied a nonthermal electron distribution function, exploring representative parameters to compare with multiwavelength observations. We further considered Kerr and dilaton black holes matched at their unstable circular photon orbits, as well as their event horizons. Results. From the comparison of GRMHD simulations, we find a wider jet opening angle and higher magnetization in the Kerr spacetime. Generally, MAD models show larger magnetic flux than SANE, as is expected. The GRRT image morphology shows differences between spacetimes due to the Doppler boosting in the Kerr spacetime. However, from pixel-by-pixel comparison, we find that in a real-world observation an imaging approach may not be sufficient to distinguish the spacetimes using the current finite resolution of the EHT. From multiwavelength emission and spectral index analysis, we find that the accretion model and spacetime have only a small impact on the spectra compared to the choice of the emission model. Matching the black holes at the unstable photon orbit or the event horizon further decreases the observed differences. [ABSTRACT FROM AUTHOR]