Gold's structure-dependent catalytic activity motivates the study of reactions on a range of gold nanostructures. Electronic structure methods used to model gold catalysis should be capable of treating atoms, clusters, nanostructures, and surfaces on an equal theoretical footing. We extend our previous density functional theory (DFT) studies of a model reaction, H-2 adsorption and dissociation on unsupported Au-3 clusters [J. Phys. Chem. C 2013, 117, 7487], to larger clusters, quasi-one-dimensional nanowires and nanoribbons, and surfaces. We focus on trends in DFT predictions made using various approximate exchange-correlation functionals. Most functionals predict qualitatively reasonable trends, i.e., decreasing adsorption energies and increasing dissociation barriers with increasing Au coordination number. However, significant quantitative differences motivate continued exploration of methods beyond the generalized gradient approximation.