Detailed structural properties of physiological bis(amino acidato)copper(II) complexes are generally unknown in solutions. This paper examines how stereochemical differences between the essential amino acid l-threonine and its diastereomer l-allo-threonine, which is rarely present in nature, may affect relative stabilities of bis(l-threoninato)copper(II) and bis(l-allo-threoninato)copper(II) in the gas phase and aqueous solution. These amino acids can bind to Cu(II) via the nitrogen and carboxylato oxygen atoms, the nitrogen and hydroxyl oxygen atoms, and the carboxylato and hydroxyl oxygen atoms. We term these coordination modes G, No, and Oo, respectively. The density functional theory (DFT) calculations with the B3LYP functional of the conformational landscapes for all possible coordination modes of both complexes revealed their very similar stability in the gas phase and in aqueous solution. The conformational analyses resulted in 196 and 267 conformers of isolated copper(II) chelates with l-threonine and l-allo-threonine, respectively. The G-G coordination mode is the most stable, both in the gas phase and aqueous solution. Very similar energy values of the lowest-energy solvated cis and trans G-G conformers in implicitly accounted water medium are in accord with the experimental results that these isomers are present in aqueous solution at physiological pH values. The transition-state structures, activation Gibbs free energies, and reaction rates calculated using DFT/B3LYP and MP2 for the transformations from the most stable cis G-G and trans Oo-G conformers to trans G-G ones for the first time reveal several alternate coordination-mode transformation mechanisms in the copper(II) complexes with amino acids other than glycine. The trans Oo-G conformers are kinetically more stable than cis G-G ones in the gas phase. The only significant difference found between the two complexes is a more suitable position of the hydroxyl group in physiological bis(l-threoninato)copper(II) to form intramolecular hydrogen bonds, which may restrain its conformational space.