Large Language Models (LLMs) have made significant advancements in sentiment analysis, yet their quality and reliability vary widely. Existing LLM evaluation studies are limited in scope, lack a comprehensive framework for integrating diverse capabilities, and fail to quantify the impact of prompt design on performance. To address these gaps, this paper introduces a set of LLM evaluation criteria with detailed explanations and mathematical formulations, aiding users in understanding LLM limitations and selecting the most suitable model for sentiment analysis. Using these criteria, we apply the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), a classic decision-making method, to rank the performance of LLMs in sentiment analysis. We evaluated six popular LLMs on three Twitter datasets covering different topics and analyzed the impact of prompt design by assessing model-prompt combinations. Additionally, a validation experiment on a publicly available annotated dataset further confirms our ranking results. Finally, our findings offer valuable insights into the evaluation and selection of LLMs for sentiment analysis.