Using the different versions of phenomenological proximity potential as well as other parametrizations within the proximity concept, we perform a detailed comparative study of fusion barriers for asymmetric colliding nuclei with asymmetry parameter as high as 0.23. In all, 12 different proximity potentials are robust against the experimental data of 60 reactions. Our detailed study reveals that the surface energy coefficient as well as radius of the colliding nuclei depend significantly on the asymmetry parameter. All models are able to explain the fusion barrier heights within ±10% on the average. The potentials due to Bass 80, AW 95, and Denisov DP explain nicely the fusion cross sections at above-as well as below-barrier energies.