The expressive power and effectiveness of large language models (LLMs) is going to increasingly push intelligent agents towards sub-symbolic models for natural language processing (NLP) tasks in human–agent interaction. However, LLMs are characterised by a performance vs. transparency trade-off that hinders their applicability to such sensitive scenarios. This is the main reason behind many approaches focusing on local post-hoc explanations, recently proposed by the XAI community in the NLP realm. However, to the best of our knowledge, a thorough comparison among available explainability techniques is currently missing, as well as approaches for constructing global post-hoc explanations leveraging the local information. This is why we propose a novel framework for comparing state-of-the-art local post-hoc explanation mechanisms and for extracting logic programs surrogating LLMs. Our experiments—over a wide variety of text classification tasks—show how most local post-hoc explainers are loosely correlated, highlighting substantial discrepancies in their results. By relying on the proposed novel framework, we also show how it is possible to extract faithful and efficient global explanations for the original LLM over multiple tasks, enabling explainable and resource-friendly AI techniques.