This research assesses the effectiveness of state-of-the-art large language models (LLMs), including ChatGPT, Llama, Aya, Jais, and ACEGPT, in the task of Arabic automated essay scoring (AES) using the AR-AES dataset. It explores various evaluation methodologies, including zero-shot, few-shot in-context learning, and fine-tuning, and examines the influence of instruction-following capabilities through the inclusion of marking guidelines within the prompts. A mixed-language prompting strategy, integrating English prompts with Arabic content, was implemented to improve model comprehension and performance. Among the models tested, ACEGPT demonstrated the strongest performance across the dataset, achieving a Quadratic Weighted Kappa (QWK) of 0.67, but was outperformed by a smaller BERT-based model with a QWK of 0.88. The study identifies challenges faced by LLMs in processing Arabic, including tokenization complexities and higher computational demands. Performance variation across different courses underscores the need for adaptive models capable of handling diverse assessment formats and highlights the positive impact of effective prompt engineering on improving LLM outputs. To the best of our knowledge, this study is the first to empirically evaluate the performance of multiple generative Large Language Models (LLMs) on Arabic essays using authentic student data.