The preservation of historical heritage buildings frequently requires the assessment of brick masonry structures. These structures exhibit complex behaviour due to the arrangement of units and the interaction between bricks and mortar. This study aims to compare two modelling techniques for simulating masonry's compressive response and understanding which technique performs better. This study employs two block-based modelling techniques: a simplified brick-to-brick model and a detailed brick-to-brick model. The block-based modelling technique was selected to capture the intricate structural details and crack patterns of masonry specimens. Wallet specimens were evaluated to understand the compressive behaviour of masonry. Two experimental benchmarks were chosen to validate the selected modelling approach. First, experimental results by Thamboo (2020), also modelled with a simplified brick-to-brick model by Zahra et al. (2021), were considered. However, to obtain numerical results comparable to the experimental ones, unrealistic input parameters had to be assumed (i.e., very low value of elastic modulus for the bricks); consequently, this benchmark was ultimately deemed unreliable. Hence, a second benchmark from Jafari (2021) was chosen which did not present such issues. Considering the effect of confinement was crucial to obtain results in agreement with experiments. The detailed brick-to-brick model, explicitly modelling each brick-and-mortar joint with solid elements and accounting for mortar confinement, proved to be the only modelling approach able to simulate the second experimental benchmark. The simplified modelling technique, considering mortar joints as zero-thickness interfaces between solid elements representing the bricks, consistently underestimated the peak loads as mortar confinement was not included. This may explain why unrealistic input parameters were used by Zahra et al. (2021) to simulate the first benchmark. In general, the post-peak behaviour was difficult to simulate. A sensitivity study was performed by varying the boundary conditions, Poisson’s ratio of mortar and integration scheme. The study on boundary conditions was performed on both the simplified and detailed models whereas the study on Poisson’s ratio and integration scheme was performed on the detailed model. The boundary conditions did not have a significant influence on the global behaviour of the specimen in the detailed or simplified models. Small variation in compressive strength and crack pattern were observed, but the effect on post-peak behaviour could not be evaluated due to numerical instability. The Poisson’s ratio of mortar was found to have a significant influence on the peak compressive strength of the masonry specimen. A higher Poisson's ratio resulted in a greater value in the peak compressive strength of masonry. A higher value of Poisson’s ratio increases the amount of confinement in mortar layers resulting in higher values of compressive strength of masonry. A high integration scheme (3×3×3) and a regular integration scheme (2×2×2) effectively captured crack propagation. On the contrary, a reduced integration scheme (1×1×1) could not do so effectively. The reason can be attributed to the higher number of integration points in the former cases which allows for better propagation of cracks. These investigations provide precious insight into the choice of modelling techniques for simulating the compressive behaviour of brick masonry. The detailed modelling technique can be implemented to study the compressive behaviour of masonry specimens if mortar confinement is accounted for. However, further effort is necessary to reduce numerical instability to simulate the post-peak response. This can be adopted further to study the influence of, for example, bond pattern, specimen thickness (e.g., multi- vs single-wythe masonry) and specimen shape (e.g. wallets, prism, core) on the compressive behaviour of masonry.