Resonant and nonresonant intermolecular vibrational energy transfers in KSCN/KSC(13)N/KS(13)C(15)N aqueous and DMF solutions and crystals are studied. Both energy-gap and temperature dependent measurements reveal some surprising results, e.g. inverted energy-gap dependent energy transfer rates and opposite temperature dependences of resonant and nonresonant energy transfer rates. Two competing mechanisms are proposed to be responsible for the experimental observations. The first one is the dephasing mechanism in which the measured energy transfer rate originates from the dephasing of the energy donor-acceptor coherence, and the second one is the phonon-compensation mechanism derived from the second order perturbation. It is found that both the nonresonant energy transfers in the liquids and resonant energy transfers in both liquids and solids can be well described by the first mechanism. The second mechanism explains the nonresonant energy transfers in one series of the solid samples very well.