Environmental tax reform (ETR), a shift from labour to carbon taxes, has been mostly modelled using general equilibrium (GE) analysis. Since a low-carbon transition will require deep transformations, one will also have to address out-of-equilibrium dynamics and increased agent heterogeneity. Unlike GE models, agent-based models (ABMs) are well equipped to deal with this. We therefore replicate a recent GE model for ETR using an agent-based approach. This process, known as "agentization", allows assessing similarities as well as differences in policy impacts between the two modelling approaches, in turn providing a test of the robustness of the GE results. We find that the agent-based model is able to replicate many results of the general equilibrium analysis, while revealing strengths and weaknesses of both model types. We discuss concrete implementation steps and difficulties experienced in the GE-ABM translation process. We illustrate the potential of ABM by extending the model in several directions. We show that heterogeneous subsistence consumption can increase the space for combining a double dividend with an equity goal, and that overall macro-economic results can conceal important distributional impacts when green preferences and labour supply elasticities vary.