Recent advancements in large language models (LLMs) have shown promise in feature engineering for tabular data, but concerns about their reliability persist, especially due to variability in generated outputs. We introduce a multi-level diagnosis and evaluation framework to assess the robustness of LLMs in feature engineering, focusing on identifying key variables, relationships, and decision boundaries for predicting target classes across diverse domains. We demonstrate that the robustness of LLMs varies significantly over different datasets, and that high-quality LLM-generated features can improve prediction performance by up to 10.52%. This work opens a new direction for assessing and enhancing the reliability of LLM-driven feature engineering.