We present comprehensive molecular dynamics results for the kinetics of surface-directed spinodal decomposition and surface enrichment in binary mixtures at wetting surfaces. We study the surface morphology and the growth dynamics of the wetting and enrichment layers. The growth law for the thickness of these layers shows a crossover from a diffusive regime to a hydrodynamic regime. We provide phenomenological arguments to understand this crossover. © 2012 Europhysics Letters Association.