Metformin (Metf), the most commonly used type 2 diabetes drug, is known to affect the cellular housekeeping of copper. Recently, we discovered that the structurally closely related propanediimidamide (PDI) shows a cellular behavior different from that of Metf. Here we investigate the binding of these compounds to copper, to compare their binding strength. Furthermore, we take a closer look at the electronic properties of these compounds and their copper complexes such as molecular orbital interactions and electrostatic potential surfaces. Our results clearly show that the copper binding energies cannot alone be the cause of the biochemical differentiation between Metf and PDI. We conclude that other factors such as pKa values and hydrophilicity of the compounds play a crucial role in their cellular activity. Metf in contrast to PDI can occur as an anion in aqueous medium at moderate pH, forming much stronger complexes particularly with Cu(II) ions, suggesting that biguanides but not PDI may induce easy oxidation of Cu(I) ions extracted from proteins. The higher hydrophobicity and the lack of planarity of PDI may further differentiate it from biguanides in terms of their molecular recognition characteristics. These different properties could hold the key to metformin's mitochondrial activity because they suggest that the drug could act at least in part as a pro-oxidant of accessible protein-bound Cu(I) ions.