This paper explores the human-centric operationalization of Automated Essay Scoring (AES) systems, addressing aspects beyond accuracy. We compare various machine learning-based approaches with Large Language Models (LLMs) approaches, identifying their strengths, similarities and differences. The study investigates key dimensions such as bias, robustness, and explainability, considered important for human-aware operationalization of AES systems. Our study shows that ML-based AES models outperform LLMs in accuracy but struggle with explainability, whereas LLMs provide richer explanations. We also found that both approaches struggle with bias and robustness to edge scores. By analyzing these dimensions, the paper aims to identify challenges and trade-offs between different methods, contributing to more reliable and trustworthy AES methods.