(1) Background: Ruthenium and osmium complexes attract increasing interest as next generation anticancer drugs. Focusing on structure-activity-relationships of this class of compounds, we report on 17 different ruthenium(II) complexes and four promising osmium(II) analogues with cinnamic acid derivatives as O,S bidentate ligands. The aim of this study was to determine the anticancer activity and the ability to evade platin resistance mechanisms for these compounds. (2) Methods: Structural characterizations and stability determinations have been carried out with standard techniques, including NMR spectroscopy and X-ray crystallography. All complexes and single ligands have been tested for cytotoxic activity on two ovarian cancer cell lines (A2780, SKOV3) and their cisplatin-resistant isogenic cell cultures, a lung carcinoma cell line (A549) as well as selected compounds on three non-cancerous cell cultures in vitro. FACS analyses and histone γH2AX staining were carried out for cell cycle distribution and cell death or DNA damage analyses, respectively. (3) Results: IC50 values show promising results, specifically a high cancer selective cytotoxicity and evasion of resistance mechanisms for Ru(II) and Os(II) compounds. Histone γH2AX foci and FACS experiments validated the high cytotoxicity but revealed diminished DNA damage-inducing activity and an absence of cell cycle disturbance thus pointing to another mode of action. (4) Conclusion: Ru(II) and Os(II) compounds with O,S-bidentate ligands show high cytotoxicity without strong effects on DNA damage and cell cycle, and this seems to be the basis to circumvent resistance mechanisms and for the high cancer cell specificity.