As reactor-level nuclear fusion experiments are approaching, a solution to the power exhaust issue in future fusion reactors is still missing. The maximum steady-state heat load that can be exhausted by the present technology is around 10 MW/m2. Different promising strategies aiming at successfully managing the power exhaust in reactor-relevant conditions such that the limit is not exceeded are under investigation, and will be tested in the Divertor Tokamak Test (DTT) experiment. Meanwhile, the design of tokamaks beyond the DTT, e.g. EU-DEMO/ARC, is progressing at a high pace. A strategy to work around the present lack of reactor-relevant data consists of exploiting modelling to reduce the uncertainty in the extrapolation in the design phase. Different simulation tools, with their own capabilities and limitations, can be employed for this purpose. In this work, we compare SOLPS-ITER, SOLEDGE2D and UEDGE, three state-of-the-art edge codes heavily used in power exhaust studies, in modelling the same DTT low-power, pure-deuterium, narrow heat-flux-width scenario. This simplified, although still reactor-relevant, testbed eases the cross-comparison and the interpretation of the code predictions, to identify areas where results differ and develop understanding of the underlying causes. Under the conditions investigated, the codes show encouraging agreement in terms of key parameters at both targets, including peak parallel heat flux (1-45%), ion temperature (2-19%), and inner target plasma density (1-23%) when run with similar input. However, strong disagreement is observed for the remaining quantities, from 30% at outer mid-plane up to a factor 4-5 at the targets. The results primarily reflect limitations of the codes: the SOLPS-ITER plasma mesh not reaching the first wall, SOLEDGE2D not including ion-neutral temperature equilibration, and UEDGE enforcing a common ion-neutral temperature. Potential improvements that could help enhance the accuracy of the code models for future applications are also discussed.