In order to build the phase diagram of Cu-Ag nanoalloys, we study a 405-atom nanoparticle by means of Monte Carlo simulations with relaxations using N-body interatomic potentials. We focus on a range of nominal concentrations for which the cluster core remains Cu-pure and the (001) facets of the outer shell exhibit two original phenomena. Within the (N,mAg-mCu,P,T) ensemble, a structural and chemical bistability is observed, which affects all the (001) facets together. For a nanoparticle assembly, this will result in a bimodal distribution of clusters, some of them having their (001) facets Cu-rich with the usual square shape, the other ones having their (001) facets Ag-rich with a diamond shape. This bistability is replaced in the (NAg,NCu,P,T) ensemble by a continuous evolution of both the structure and the concentration of the (001) facets from Cu-rich square-shaped to Ag-rich diamond-shaped facets as the number of Ag atoms increases. For a nanoparticle assembly, this will result in an unimodal distribution of the cluster population concerning the properties of the (001) facets. This comparison between pseudo grand canonical and isothermal-isobaric results shows that the distribution of a population of bimetallic nanoparticles depends strongly on the conditions under it is elaborated.