Concurrent programs are prone to data races due to nondeterministic thread interleavings, yet traditional detection tools still suffer from inherent trade-offs among precision, coverage, and applicability. Can Large Language Models (LLMs) offer a viable alternative? While LLMs have demonstrated strong code understanding capabilities, their effectiveness in concurrent program analysis remains largely unexplored. We present a comprehensive empirical study comparing LLM-based approaches with traditional static and dynamic analysis tools for data race detection. Our evaluation spans over 3,950 concurrent program files (1.4M+ LoC) from three complementary sources: standard benchmarks, Linux-kernel verification tasks, and large-scale real-world projects. We systematically evaluate multiple LLMs under direct prompting, Chain-of-Thought (CoT) reasoning, and a multi-stage agent workflow for race detection. We further investigate the impact of model families and parameter scales (4B–235B), and compare the optimal configuration against state-of-the-art concurrency analysis tools (e.g., TSan, OpenRace, and SVF). Results show that, under our evaluation setting, the LLMbased agent achieves the best F1 score with significantly higher precision and comparable recall, while requiring neither compilation nor execution. We also analyze cost-efficiency trade-offs and reveal that LLM hallucinations and traditional tool false alarms exhibit fundamentally different code patterns, indicating that combining generative reasoning with conventional analysis is a promising direction for advancing concurrent program analysis.