The molecular mechanisms of toxicity and cellular transport of anticancer metallodrugs, including platinum-based agents, have not yet been fully elucidated. The aim of our study was to investigate the relevance of copper transporters (CTR1 and ATP7A/B), organic cation transporters (OCT2) and the multidrug and toxin extrusion proteins (MATE) in the intracellular accumulation of a novel organometallic cytotoxic Au(III) compound in cancer cells in comparison to cisplatin. Specifically, the synthesis and characterization of the gold complex [Au(pyb-H)(PPh2Ar)Cl]PF6 (PPh2Ar = 3-[4-(diphenylphosphino)phenyl]-7-methoxy-2H-chromen-2-one] (1), featuring a coumarin ligand endowed with “smart” fluorescence properties, have been achieved. Initially, the cytotoxic effects of both cisplatin and 1 were studied in a small panel of human cancer cells, and against a non-tumorigenic cell line in vitro. Thus, the human ovarian cancer cell line A2780 and its cisplatin resistant variant A2780cisR, were selected, being most sensitive to the treatment of the gold complex. Co-incubation of the metallodrugs with CuCl2 (a CTR1 substrate) increased the cytotoxic effects of both the Au(III) complex and cisplatin; while co-incubation with cimetidine (inhibitor of OCT2 and MATE) showed some effect only after 72 h incubation. ICP-MS (Inductively Coupled Plasma Mass Spectrometry) analysis of the cell extracts showed that co-incubation with CuCl2 increases Au and Cu accumulation in both cancer cell lines, in accordance with the enhanced antiproliferative effects. Conversely, for cisplatin, no increase in Pt content could be observed in both cell lines after co-incubation with either CuCl2 or cimetidine, excluding the involvement of CTR1, OCT2, and MATE in drug accumulation and overall anticancer effects. This result, together with the evidence for increased Cu content in A2780 cells after cisplatin co-treatment with CuCl2, suggests that copper accumulation is the reason for the observed enhanced anticancer effects in this cell line. Moreover, metal uptake studies in the same cell lines indicate that both 1 and cisplatin are not transported intracellularly by CTR1 and OCT2. Finally, preliminary fluorescence microscopy studies enabled the visualization of the sub-cellular distribution of the gold compound in A2780 cells, suggesting accumulation in specific cytosolic components/organelles.