This paper presents a rigorous evaluation of Real-to-Sim parameter estimation approaches for fabric manipulation in robotics. The study systematically assesses three state-of-the-art approaches, namely two differential pipelines and a data-driven approach. We also devise a novel physics-informed neural network approach for physics parameter estimation. These approaches are interfaced with two simulations across multiple Real-to-Sim scenarios (lifting, wind blowing, and stretching) for five different fabric types and evaluated on three unseen scenarios (folding, fling, and shaking). We found that the simulation engines and the choice of Real-to-Sim approaches significantly impact fabric manipulation performance in our evaluation scenarios. Moreover, PINN observes superior performance in quasi-static tasks but shows limitations in dynamic scenarios.