This study explores the use of large language models (LLMs) to generate feedback on essay-type assignments in Higher Education. Drawing on a seminal feedback framework, it examines the pedagogical and psychological effectiveness of LLM-generated feedback across three cohorts of MBA, MSc, and undergraduate students. Methods included linguistic analysis and student surveys to assess student perceptions of LLM-generated feedback. Findings suggest that students appreciate the clarity and specificity of LLM-generated feedback, although recurring lexical patterns and occasional logical inconsistencies may reduce perceived authenticity. While some students preferred human input, the majority favoured a hybrid model combining the speed and consistency of LLMs with the emotional resonance and motivational impact of human feedback. This study addresses a gap in the literature by examining how students perceive LLM-generated feedback, an area that remains underexplored despite the rapid integration of AI tools in Higher Education.