We examine the structure of densely grafted polymer layers grown from the surfaces of spherical nanoparticles over a broad range of graft densities and chain lengths. Dynamics light scattering (DLS) experiments show that the hydrodynamic thickness of the polymer layer, h, scales as h infinity N-4/5 for short chains and high grafting densities, that is, in the concentrated polymer brush (CPB) regime, whereas h infinity N-3/5 for long enough chains (semidilute polymer brush, SDPB). The mean field theory of Wijmans and Zhulina is able to collapse approximately all of our data and those in the existing literature (even on other polymers) into an apparently universal form. From these findings. we conclude that the result h infinity N-4/5 for the CPB is an intermediate crossover scaling, relevant to particles of finite curvature, analogous to the h infinity N observed for concentrated flat brushes. Second, the scaling h infinity N-3/5 uniquely reflects the increased space available to the chain segments as one proceeds away from a curved grafting surface. Under these situations, the chains experience less packing frustration as compared to a planar brush, and the semidilute polymer brush shows scaling behavior analogous to chains in good solvent, even though the chains are much more extended.