This study examines the application of ordinal classification methods in transformer-based automated essay scoring (AES) models and compares them with conventional regression-based approaches. We evaluate our models in various settings, including the types of pre-trained encoders, essay prompts, and scoring scales. Our results show that the ordinal classification models perform comparably to the regression models regarding the overall QWK score and across different score ranges, as evidenced by centrality measures and qualitative analysis.