Several advanced models for multi-temperature vibrational energy relaxation rates are implemented to study adiabatic bath relaxation in carbon dioxide, among them a hybrid model based on state-to-state relaxation rates, the model based on the rigorous Chapman-Enskog theory, and modifications of the Landau-Teller (LT) models. Different sets of rate coefficients for vibrational energy transitions (Schwartz, Slawsky and Herzfeld (SSH) theory, forced harmonic oscillator (FHO) model) are used as well as various techniques for the relaxation time evaluation. Based on isothermal bath simulations it is found that the FHO model provides good agreement with experimentally measured relaxation times. Assessment of relaxation models shows that the three-temperature model based on the Chapman-Enskog theory yields excellent agreement with the detailed hybrid approach while being more computationally efficient; two-temperature models and modifications of the LT formulas cannot provide reliable description of intermode exchanges in polyatomic gases. The choice of the model for transition probabilities is crucial for identifying key relaxation mechanisms. When the FHO model is applied, strongly coupled relaxation in all CO2 modes is found whereas the model of SSH yields overpredicted relaxation rate in the symmetric-bending mode and almost uncoupled slow relaxation in the asymmetric mode. Possible ways for further model validation under glow discharge conditions are discussed.