We present a quantitative study of the catalytic activity of well-defined faceted gold-palladium nanoalloys which are immobilized on cationic spherical polyelectrolyte brushes. The spherical polyelectrolyte brush particles used as carriers for the nanoalloys consist of a solid polystyrene core onto which cationic polyelectrolyte chains of 2-aminoethyl methacrylate are attached. Au/Pd nanoalloy particles with sizes in the range from 1 to 3 nm have been generated which are homogeneously distributed on the surface of the spherical polyelectrolyte brushes. The reduction of 4-nitrophenol has been chosen as a well-controlled model reaction allowing us to determine the catalytic activity of the nanoalloys as a function of the Au/Pd composition. The adsorption behavior was studied by Langmuir-Hinshelwood kinetics. We find a pronounced maximum of the catalytic activity at 75 molar % Au. A comparison of gold, platinum, palladium and gold-palladium alloy nanoparticles is made in terms of Langmuir-Hinshelwood kinetics. Density functional calculations for Au/Pd clusters with up to 38 atoms show that the density of states at the Fermi level increases with increasing Pd content, and that the highest occupied orbitals are associated with Pd atoms. The calculations confirm that small changes in the atomic arrangement can lead to pronounced changes in the particles' electronic properties, indicating that the known importance of surface effects is further enhanced in nanoalloys.