The energy landscape and kinetics of medium-sized Ag-Au and Ag-Ni nanoalloy particles are explored via a discrete path sampling approach, focusing on rearrangements connecting regions differing in chemical order. The highly miscible Ag27Au28 supports a large number of nearly degenerate icosahedral homotops. The transformation from reverse core-shell to core-shell involves large displacements away from the icosahedron through elementary steps corresponding to surface diffusion and vacancy formation. The immiscible Ag42Ni13 naturally forms an asymmetric core-shell structure, and about 10 eV is required to extrude the nickel core to the surface. The corresponding transformation occurs via a long and smooth sequence of surface displacements. For both systems the rearrangement kinetics exhibit Arrhenius behavior. These results are discussed in the light of experimental observations.