Measuring leaf areas is a critical task in plant biology. Automatic leaf area estimation from a 3D point cloud is usually done via meshing techniques or parametric surface modeling. However, there is currently no consensus on the best method because of little comparative evaluation of the techniques. In this paper, we provide evidence about the performance of each approach through a comparative study of four meshing methods and two parametric model fitting techniques applied in the plant sciences. We identified six criteria on either the leaf shape (length/width ratio, curviness, concavity) or the acquisition process (sampling density, noise, holes) which can affect the robustness of the six selected methods. We generated synthetic point clouds covering each criterion and used them to qualitatively and quantitatively evaluate the six approaches. This study allows us to highlight the benefits and drawbacks of each method and evaluate its appropriateness in a given scenario.