To be able to propose experimental tests to distinguish elongated dihydrogen transition-metal complexes from compressed dihydride transition-metal complexes, a thorough density functional study of the electronic structure in combination with quantum nuclear dynamics calculations have been performed for complexes [Cp*Ru(H2PCH2PCH2(H2)]+ and [CpRe(CO)2H2]. The results of this study suggest that elongated dihydrogen complexes and compressed dihydride complexes have different properties and that it should be possible to distinguish between them experimentally. In particular, different behavior is predicted with respect to 1) the sign of the isotope geometric effect on the H-H distance at 0 K, 2) the temperature dependence of the H-H distance, and 3) the temperature dependence of the H-D spin-spin coupling constant in 1H NMR spectroscopy.