Online Social Networks (OSNs) widely adopt content moderation to mitigate the spread of abusive and toxic discourse. Nonetheless, the real effectiveness of moderation interventions remains unclear due to the high cost of data collection and limited experimental control. The latest developments in Natural Language Processing pave the way for a new evaluation approach. Large Language Models (LLMs) can be successfully leveraged to enhance Agent-Based Modeling and simulate human-like social behavior with unprecedented degree of believability. Yet, existing tools do not support simulation-based evaluation of moderation strategies. We fill this gap by designing a LLM-powered simulator of OSN conversations enabling a parallel, counterfactual simulation where toxic behavior is influenced by moderation interventions, keeping all else equal. We conduct extensive experiments, unveiling the psychological realism of OSN agents, the emergence of social contagion phenomena and the superior effectiveness of personalized moderation strategies.