The interaction between two spherical polymer brushes in solvents of Variable quality is studied by molecular dynamics simulation and by self-consistent field theory, varying both the radius of the spherical particles and their distance, as well as the grafting density and the chain length of the end-grafted flexible polymer chains. Both the potential of mean force between the particles as a function of their distance is computed, for various choices of the parameters mentioned above, and the structural characteristics are discussed (density profiles, average end-to-end distance of grafted chains, etc.) It is found that for rather short chain lengths and not too large grafting densities, isolated spherical brushes in the poor solvent regime exhibit incomplete coverage of the nanoparticle, rather than a complete coverage, i.e., a core-shell structure where the nanoparticle is covered homogeneously by a dense polymeric film. This latter case occurs for long chains and/or high grafting densities. When two Such incompletely covered spherical brushes are close by, they form a dense liquid bridge from the collapsed grafted chains, creating an elongated spherocylindrical structure. Then the potential of mean force exhibits a deep minimum, of order 100 kappa T-B. However, these structures where two spherical brushes are tightly bound together are out structures. Near the Theta point, a weak binding of spherical nanoparticles which stay essentially undeformed occurs.