The deployment of Large Language Models (LLMs) in production environments requires efficient inference serving systems that balance throughput, latency, and resource utilization. This paper presents a comprehensive empirical evaluation of two prominent open-source LLM serving frameworks: vLLM and HuggingFace Text Generation Inference (TGI). We benchmark these systems across multiple dimensions including throughput performance, end-to-end latency, GPU memory utilization, and scalability characteristics using LLaMA-2 models ranging from 7B to 70B parameters. Our experiments reveal that vLLM achieves up to 24x higher throughput than TGI under high-concurrency workloads through its novel PagedAttention mechanism, while TGI demonstrates lower tail latencies for interactive single-user scenarios. We provide detailed performance profiles for different deployment scenarios and offer practical recommendations for system selection based on workload characteristics. Our findings indicate that the choice between these frameworks should be guided by specific use-case requirements: vLLM excels in high-throughput batch processing scenarios, while TGI is better suited for latency-sensitive interactive applications with moderate concurrency.