Given the advancements in conversational artificial intelligence, the evaluation and assessment of Large Language Models (LLMs) play a crucial role in ensuring optimal performance across various conversational tasks. In this paper, we present a comprehensive study that thoroughly evaluates the capabilities and limitations of five prevalent LLMs: Llama, OPT, Falcon, Alpaca, and MPT. The study encompasses various conversational tasks, including reservation, empathetic response generation, mental health and legal counseling, persuasion, and negotiation. To conduct the evaluation, an extensive test setup is employed, utilizing multiple evaluation criteria that span from automatic to human evaluation. This includes using generic and task-specific metrics to gauge the LMs' performance accurately. From our evaluation, no single model emerges as universally optimal for all tasks. Instead, their performance varies significantly depending on the specific requirements of each task. While some models excel in certain tasks, they may demonstrate comparatively poorer performance in others. These findings emphasize the importance of considering task-specific requirements and characteristics when selecting the most suitable LM for conversational applications.