Simulation-based inference (SBI) has become an increasingly important framework for parameter estimation in models for which simulation is feasible, including cases where likelihood evaluation is unavailable or costly. While recent work has introduced benchmark frameworks to compare likelihood-free methods, these studies often do not account for structural features such as heavy-tails or discreteness. In this article, we investigate how the performance of likelihood-free inference methods depends on these structural properties. We consider four approaches: MLE, NBE, EOT and AW--NBE and evaluate them using simulations. This study highlights the importance of carefully selecting evaluation tools in the presence of extremes and discrete data.