Refactoring is a software engineering practice that aims to improve code quality without altering program behavior. Although automated refactoring tools have been extensively studied, their practical applicability remains limited. Recent advances in Large Language Models (LLMs) have introduced new opportunities for automated code refactoring. The evaluation of such an LLM-driven approach, however, leaves unanswered questions about its effects on code quality. In this paper, we present a comprehensive empirical study on LLM-driven refactoring using GPT-4o, applied to 100 Python classes from the ClassEval benchmark. Unlike prior work, our study explores a wide range of class-level refactorings inspired by Fowler's catalog and evaluates their effects from three complementary perspectives: (i) behavioral correctness, verified through unit tests; (ii) code quality, assessed via Pylint, Flake8, and SonarCloud; and (iii) readability, measured using a state-of-the-art readability tool. Our findings show that GPT-4o generally produces behavior-preserving refactorings that reduce code smells and improve quality metrics, albeit at the cost of decreased readability. Our results provide new evidence on the capabilities and limitations of LLMs in automated software refactoring, highlighting directions for integrating LLMs into practical refactoring workflows.