A comparative Study on the conversion of an energetic H+ beam inside a cell neutralizer filled with hydrogen gas target is conducted by two different methods to determine the maximum beam neutralization efficiency and corresponding optimal gas thickness in terms of beam energy, ranging from 1 keV to 10 MeV. One method analytically solves the equations of particle flux with a deterministic response. The other uses the random collisional probability based on the Monte Carlo simulation with non-deterministic response, which is implemented by COMSOL software. Effective reactions of charge exchange and reionization are commonly considered in both methods with the energy-depended collisional cross section. The results obtained from the two methods are compared, demonstrating good fitness with a mean difference of ±1.5 %. This acceptive difference arises often due to statistical errors that occur in the Monte Carlo calculations. Additionally, a close agreement is found between calculated and measured efficiencies.