The performance of force-based and displacement-based seismic assessment methods for the life-safety limit state check of out-of-plane loaded unreinforced masonry walls is evaluated on the basis of refined numerical simulations. For this purpose, a discrete element model of a vertically spanning wall is built and validated against experimental results from static and dynamic test conditions. The model is then analysed for a large range of wall configurations. For each configuration, a static pushover analysis and a series of incremental dynamic analyses are run, the latter permitting to determine the capacity of the wall under dynamic loading. The accuracy of the assessment methods in predicting the acceleration at which the walls collapse is evaluated. It is found that the displacement-based method is more accurate, robust, and safe than the force-based method. The comparison also shows that for walls characterised by a relatively high ratio of axial load to Euler's critical load, both assessment methods lead to an overestimation of the wall capacity. As a remedy, a modification to the methods based on a recently developed mechanical model is put forward and tested. For the force-based method, it is additionally suggested to set for walls with relatively high overburden ratios the behaviour factor equal to 1. To ensure reproducibility of this study, all input and output files of the numerical simulations are made publicly available.