The bending-corrected rotating linear model (BCRLM) is used to investigate the reaction of neon with H-2(+) (v=0-3) using three different fits to the ab initio potential-energy surface computed by Urban, Jaquet, and Staemmler. Numerous long-lived scattering resonances are found for each surface. The number and position of these scattering resonances are found to be sensitive to the relatively small differences among these three surfaces. These BCRLM results demonstrate how the rich resonance structure that appears in the partial cross sections is washed out in the total cross section. The integrated rates for reactivity from v=0 and 1 are nearly identical for all three potential-energy surfaces over a wide range of temperatures. However, the integrated rates from v=2 and 3 exhibit significant differences among the potential-energy surfaces. A vibrationally adiabatic hyperspherical model of the trapped resonance states provides insight into the nature and contribution of these resonances to reactive scattering. The more accurate of the three fits to the ab initio potential-energy surface (obtained using the functional form of Aguado and Paniagua) is also used to obtain converged results for total angular momentum J=0 employing the adiabatically adjusting, principal axis, hyperspherical (APH) formulation of Pack and Parker for quantum reactive scattering in three dimensions (3D). An eigenlifetime analysis of these 3D scattering results reveals numerous resonances with lifetimes of 1 ps or more. While this resonance structure is sensitive to the details of the potential energy surface, with appropriate Gaussian averaging over the total scattering energy, the cumulative reaction probabilities (CRPs) are not very sensitive to changes in the potential energy surface. Moreover, these quantum CRPs agree rather well with CRPs predicted using variational Rice-Ramsperger-Kassel-Marcus (RRKM) calculations.