Intelligent drug recommendation based on Electronic Health Records (EHRs) is critical for improving the quality and efficiency of clinical decision-making. By leveraging large-scale patient data, drug recommendation systems can assist physicians in selecting the most appropriate medications according to a patient's medical history, diagnoses, laboratory results, and comorbidities. Recent advances in large language models (LLMs) have shown remarkable capabilities in complex reasoning and medical text understanding, making them promising tools for drug recommendation tasks. However, the application of LLMs for Chinese clinical medication recommendation remains largely unexplored. In this work, we conduct a systematic investigation of LLM-based methodologies for Chinese discharge medication recommendation. We evaluate several representative LLM families (GLM, Llama, Qwen) under a unified methodological framework including zero-shot prompting, in-context learning, chain-of-thought prompting, and supervised fine-tuning using LoRA. We analyze model behavior across reasoning styles, error patterns, domain adaptation mechanisms, and robustness. Experimental results show that while supervised fine-tuning improves model performance, there remains substantial room for improvement, with the best model achieving the F1 score of 0.5648 and Jaccard score of 0.4477. Our findings highlight both the potential and limitations of LLMs for Chinese drug recommendation.