Molecular dynamics simulations were performed to investigate the performance of three deep eutectic solvents (DESs) in the separation of acid gases from natural gas. To evaluate the efficiency of these DESs, their performance was compared with that of the conventional methyl diethanolamine (MDEA) system. For this purpose, the acidic DES (phenyl propionic acid and choline chloride; with 67 mol % Phpr), same acidic DES accompanied by boron-nitride nanotube (Nano-DES), and acidic DES with methyl diethanolamine (DES-MDEA) were considered. The solubility selectivity and diffusion selectivity were evaluated and compared to those of MDEA system. The Nano-DES system showed the best performance in terms of solubility selectivity of H2S over CH4, while the high solubility selectivity of CO2 over CH4 was obtained for pure DES systems. Likewise, the aqueous MDEA and the DES-MDEA systems exhibited the largest diffusivity selectivity of H2S over CH4 and CO2 over CH4, respectively. These results were rationalized and explained by analyzing the density profile and interaction energies. Besides, the radial and spatial distribution function, Gaussian normalized distribution of measured dipole moment of species, and the orientation of dipole moment species were investigated to explain the obtained results. Furthermore, dynamical properties such as mean square displacement and corrected diffusion coefficient of species indicated that CO2 molecules diffuse faster than H2S for studied systems except for aqueous MDEA. Likewise, the diffusion coefficient of H2S and CO2 in the considered systems follow the trends Nano-DES < DES-MDEA < DES < MDEA < aqueous MDEA, and DES < DES-MDEA < MDEA < Nano-DES < aqueous MDEA in the liquid phase, respectively.