Four Ru-Pd heterobimetallic complexes, each one in two different coordination modes (NNSS and NS) having metals connected by a binucleating dialkyldithiooxamidate [N(R)SC-CS(R)N] [R = methyl, ethyl, n-butyl and isopropyl], were prepared by reacting the monochelate [(trinpropyl-phosphine)ClPd(HR2C2N2S2κ-S,S-Pd)] with [(η6-p-cymene)RuCl2]2. Furthermore, two palladium homobimetallic complexes having two (trinpropyl-phosphine)ClPd moieties joined by a diethyldithiooxamidate in both κ-N,S Pd, κ-N',S' Pd' and κ-N,N' Pd, κ-S,S' Pd' coordination modes were synthesized. For both kinds of complexes, homo- and heterobimetallic, at room temperature and in chloroform solution, the NNSS coordination mode (kinetic compounds) turns out to be unstable and therefore the resulting complexes rearrange into a thermodynamically more stable form (NS coordination mode). The crystal structures of [(trinpropyl-phosphine)ClPd]2[μ-(ethyl)2-DTO κ-N,S Pd, κ-N',S' Pd'] (2) and [(η6-p-cymene)ClRu][μ-(methyl)2-DTO κ-N,S Ru, κ-N,S Pd] [(trinpropyl-phosphine)ClPd] (1c) were determined by solid state X-ray crystallography. Moreover, the higher stability of the thermodynamic species in the heterobimetallic complexes (Ru-Pd) was evaluated by means of computational studies in accordance with the maximum hardness principle. All stable NS complexes (i.e.1c-4c, 2 and the previously reported homobimetallic Ru complex 3) were tested against two leukemia cell lines, namely the drug-sensitive CCRF-CEM cell line and its multidrug-resistant sub-cell line CEM/ADR5000 showing anti-proliferative activity in the low micromolar range (∼1-5 μM) and micromolar range (∼10-25 μM), respectively. In addition, these complexes efficaciously block at least two out of the three proteolytic activities of the tumor target 20S proteasome, with heterobimetallic complex 3c and homobimetallic complex 3 possessing the best inhibitory profile.