Large language models have recently been proposed as tools for automated essay scoring, but their agreement with human grading remains unclear. In this work, we evaluate how LLM-generated scores compare with human grades and analyze the grading behavior of several models from the GPT and Llama families in an out-of-the-box setting, without task-specific training. Our results show that agreement between LLM and human scores remains relatively weak and varies with essay characteristics. In particular, compared to human raters, LLMs tend to assign higher scores to short or underdeveloped essays, while assigning lower scores to longer essays that contain minor grammatical or spelling errors. We also find that the scores generated by LLMs are generally consistent with the feedback they generate: essays receiving more praise tend to receive higher scores, while essays receiving more criticism tend to receive lower scores. These results suggest that LLM-generated scores and feedback follow coherent patterns but rely on signals that differ from those used by human raters, resulting in limited alignment with human grading practices. Nevertheless, our work shows that LLMs produce feedback that is consistent with their grading and that they can be reliably used in supporting essay scoring.