Thinking Large Language Models (LLMs) generate explicit intermediate reasoning traces before final answers, potentially improving transparency, interpretability, and solution accuracy for code generation. However, it remains unclear which trace characteristics are informative and the quality of the reasoning chains. In this paper, we present an empirical study examining the reasoning processes and the quality of thinking LLMs on code generation tasks. We evaluate six state-of-the-art reasoning LLMs (DeepSeek-R1, OpenAI-o3-mini, Claude-3.7-Sonnet, Gemini-2.0-Flash-Thinking, Gemini-2.5-Flash, and Qwen-QwQ) on 100 BigCodeBench code generation tasks (600 model–task instances; 3,772 reasoning steps). To characterize reasoning-chain structure, we measure step count and per-step verbosity, and compare successful versus failed attempts under difficulty stratification (Hard vs. Non-Hard). We further perform a 21-participant human evaluation of reasoning quality across three dimensions: efficiency, logical consistency, and completeness, and we build a taxonomy of problematic reasoning patterns. We find the model- and difficulty-dependent relationship between step count and success, and verbosity is not a reliable correctness signal. Human analysis indicates that completeness issues dominate failures (44.5%), most often due to missed edge cases and boundary conditions, and incompleteness is a stronger predictor of failure on Hard tasks than on Non-Hard tasks (𝜌 = −0.219 vs. 𝜌 = −0.096).