Measuring leaf area is a critical task in plant biology. Meshing techniques, parametric surface modelling and implicit surface modelling allow estimating plant leaf area from acquired 3D point clouds. However, there is currently no consensus on the best approach because of little comparative evaluation. In this paper, we provide evidence about the performance of each approach, through a comparative study of four meshing, three parametric modelling and one implicit modelling methods. All selected methods are freely available and easy to use. We have also performed a parameter sensitivity analysis for each method in order to optimise its results and fully automate its use. We identified nine criteria affecting the robustness of the studied methods. These criteria are related to either the leaf shape (length/width ratio, curviness, concavity) or the acquisition process (e.g. sampling density, noise, misalignment, holes). We used synthetic data to quantitatively evaluate the robustness of the selected approaches with respect to each criterion. In addition we evaluated the results of these approaches on five tree and crop datasets acquired with laser scanners or photogrammetry. This study allows us to highlight the benefits and drawbacks of each method and evaluate its appropriateness in a given scenario. Our main conclusion is that fitting a Bézier surface is the most robust and accurate approach to estimate plant leaf area in most cases.