In this paper we study the theoretical uncertainties in the determination of the top-quark mass using next-to-leading-order (NLO) generators interfaced to parton showers (PS) that have different levels of accuracy. Specifically we consider three generators: one that implements NLO corrections in the production dynamics, one that includes also NLO corrections in top decay in the narrow width approximation, and one that implements NLO corrections for both production and decay including finite-width and interference effects. Since our aim is to provide an assessment of the uncertainties of purely theoretical origin, we consider simplified top-mass related observables that are broadly related to those effectively used by experiments, eventually modelling experimental resolution effects with simple smearing procedures. We estimate the differences in the value of the extracted top mass that would occur due to the use of the three different NLO generators, to the variation of scales, to the choice of parton distribution functions and to the matching procedure. Furthermore, we also consider differences due to the shower and to the modelling of non-perturbative effects by interfacing our NLO generators to both Pythia8.2 and Herwig7.1, with various settings. We find very different results depending upon the adopted shower model. While with Pythia8.2 we find moderate differences between the different NLO+PS generators, with Herwig7.1 we find very large ones. Furthermore, the differences between Pythia8.2 and Herwig7.1 generators are also remarkably large.