Given the forthcoming availability of Sentinel-2 (S2) images, this paper provides a systematic comparison of retrieval accuracy and processing speed of a multitude of parametric, non-parametric and physically-based retrieval methods using simulated S2 data. An experimental field dataset (SPARC), collected at the agricultural site of Barrax (Spain), was used to evaluate different retrieval methods on their ability to estimate leaf area index (LAI). With regard to parametric methods, all possible band combinations for several two-band and three-band index formulations and a linear regression fitting function have been evaluated. From a set of over ten thousand indices evaluated, the best performing one was an optimized three-band combination according to (ρ560-ρ1610-ρ2190)/(ρ560+ρ1610+ρ2190) with a 10-fold cross-validation RCV2 of 0.82 (RMSECV: 0.62). This family of methods excel for their fast processing speed, e.g., 0.05s to calibrate and validate the regression function, and 3.8s to map a simulated S2 image. With regard to non-parametric methods, 11 machine learning regression algorithms (MLRAs) have been evaluated. This methodological family has the advantage of making use of the full optical spectrum as well as flexible, nonlinear fitting. Particularly kernel-based MLRAs lead to excellent results, with variational heteroscedastic (VH) Gaussian Processes regression (GPR) as the best performing method, with a RCV2 of 0.90 (RMSECV: 0.44). Additionally, the model is trained and validated relatively fast (1.70s) and the processed image (taking 73.88s) includes associated uncertainty estimates. More challenging is the inversion of a PROSAIL based radiative transfer model (RTM). After the generation of a look-up table (LUT), a multitude of cost functions and regularization options were evaluated. The best performing cost function is Pearson's χ-square. It led to a R2 of 0.74 (RMSE: 0.80) against the validation dataset. While its validation went fast (0.33s), due to a per-pixel LUT solving using a cost function, image processing took considerably more time (01:01:47). Summarizing, when it comes to accurate and sufficiently fast processing of imagery to generate vegetation attributes, this paper concludes that the family of kernel-based MLRAs (e.g. GPR) is the most promising processing approach.