We have constructed model Hamiltonians for AuPt/Pt(111) and AuPd/Pd(111) surface alloys based on the cluster expansion method and density functional theory. Using these cluster expansions in Monte Carlo simulations, we have calculated the size and shape distributions of Pt and Pd ensembles in these two materials for a range of compositions and temperatures. We report on and explain the results of our simulations in terms of the differing interatomic interactions present in each alloy. Through the use of electronic structure calculations, we find that in AuPt, homonuclear Pt-Pt interactions are favored over heteronuclear Au-Pt interactions, while in AuPd the opposite is true. Accordingly, our simulations show that Pd prefers to form small, isolated ensembles with extended shapes, and Pt prefers to agglomerate and form larger ensembles with compact shapes.