This study presents a systematic comparison of three approaches for the analysis of mental health text using large language models (LLMs): prompt engineering, retrieval augmented generation (RAG), and fine-tuning. Using LLaMA 3, we evaluate these approaches on emotion classification and mental health condition detection tasks across two datasets. Fine-tuning achieves the highest accuracy (91% for emotion classification, 80% for mental health conditions) but requires substantial computational resources and large training sets, while prompt engineering and RAG offer more flexible deployment with moderate performance (40-68% accuracy). Our findings provide practical insights for implementing LLM-based solutions in mental health applications, highlighting the trade-offs between accuracy, computational requirements, and deployment flexibility.