In this paper we study the production of a heavy charged Higgs boson in association with heavy quarks at the LHC in the two-Higgs-doublet model. We present for the first time fully-differential results obtained in the four-flavour scheme at NLO accuracy, both at fixed order and including the matching with parton showers. Relevant differential distributions are studied for two values of the charged boson mass and a thorough comparison is performed between predictions obtained in the four- and five-flavour schemes. We show that the agreement between the two schemes is improved by NLO(+PS) corrections for observables inclusive in the degrees of freedom of bottom quarks. We argue that the four-flavour scheme leads to more reliable predictions, thanks to its accurate description of the bottom-quark kinematics and its small dependence on the Monte Carlos, which in turn is rather large in the five-flavour scheme. A detailed set of recommendations for the simulation of this process in experimental analyses at the LHC is provided.