(1) Background: Since the discovery of cisplatin’s cytotoxic properties, platinum(II) compounds have attracted much interest in the field of anticancer drug development. Over the last few years, classical structure–activity relationships (SAR) have been broken by some promising new compounds based on platinum or other metals. We focus on the synthesis and characterization of 17 different complexes with β-hydroxydithiocinnamic acid esters as O,S bidendate ligands for nickel(II), palladium(II), and platinum(II) complexes. (2) Methods: The bidendate compounds were synthesized and characterized using classical methods including NMR spectroscopy, MS spectrometry, elemental analysis, and X-ray crystallography, and their cytotoxic potential was assessed using in vitro cell culture assays. Data were compared with other recently reported platinum(II), ruthenium(II), and osmium(II) complexes based on the same main ligand system. (3) Results: SAR analyses regarding the metal ion (M), and the alkyl-chain position (P) and length (L), revealed the following order of the effect strength for in vitro activity: M > P > L. The highest activities have Pd complexes and ortho-substituted compounds. Specific palladium(II) complexes show lower IC50 values compared to cisplatin, are able to elude cisplatin resistance mechanisms, and show a higher cancer cell specificity. (4) Conclusion: A promising new palladium(II) candidate (Pd3) should be evaluated in further studies using in vivo model systems, and the identified SARs may help to target platinum-resistant tumors.