More than a decade ago the Fermi Large Area Telescope detected a GeV gamma-ray excess originating from the Galactic center. The origin of this Galactic Center Excess (GCE) remains a topic of scientific debate. The leading hypotheses explaining its nature are 1) a population of dim and unresolved millisecond pulsars or 2) dark matter annihilation. Each gamma-ray analysis depends on assumptions about background modelling. Hence, the question arises: how does the model used for the analysis affect the consequent interpretations? Are instrumental and background model uncertainties taken into account? When different models lead to different conclusions, there may be a general gap between the model space and reality that influences our conclusions. In this talk, we report the results of our study, showing that DeepEnsemble Networks can robustly detect the background components and the GCE in all model iterations while the predicted emission associated with the background components is consistent with the outcome of a traditional likelihood analysis. However, the reconstructed composition of the GCE is model-dependent. It is likely biased by the presence of a reality gap. We assess the severity of such a gap for each model instance using the One-Class Deep Support Vector Data Description method, and we show that it persists across all iterations. Our work clearly demonstrates the limitations of analyses aiming at characterizing the GCE's nature as soon as a reality gap is an intrinsic issue.