We study the theoretical uncertainties in the determination of the top-quark mass using next-to-leading-order (NLO) generators, that describe the top-quark decay at different levels of accuracy, interfaced to parton showers (PS). Specifically we consider one generator that implements NLO corrections only in the production dynamics, one that also takes them into account in the top-quark decay in the narrow width approximation (NWA) and one that implements them exactly, including finite-width and interference effects. We aim at assessing the errors in top-mass determinations of purely theoretical origin. We do so by measuring relative peak position shifts of $Wb$-jet mass distributions. Besides the theoretical errors due to the use of less accurate NLO+PS generators, we also explore uncertainties related to shower and modelling of non-perturbative effects by comparing the results obtained by interfacing our generators to both Pythia and Herwig shower Monte Carlos (SMCs).