Two relatively new approaches to neutron cross section data evaluation are described. They are known collectively as Unified Monte Carlo (versions UMC-G and UMC-B). Comparisons are made between these two methods, as well as with the well-known generalized least-squares (GLSQ) technique, through the use of simple, hypothetical (toy) examples. These new Monte Carlo methods are based on stochastic sampling of probability functions that are constructed with the use of theoretical and experimental data by applying the principle of maximum entropy. No further assumptions are involved in either UMC-G or UMC-B. However, the GLSQ procedure requires the linearization of non-linear terms, such as those that occur when cross section ratio data are included in an evaluation. It is shown that these two stochastic techniques yield results that agree well with each other, and with the GLSQ method, when linear data are involved, or when the perturbations due to data discrepancies and nonlinearity effects are small. Otherwise, there can be noticeable differences. The present investigation also demonstrates, as observed in earlier work, that the least-squares approach breaks down when these conditions are not satisfied. This paper also presents an actual evaluation of the 55Mn(n,γ)56Mn neutron dosimetry reaction cross section in the energy range from 100 keV to 20 MeV, which was performed using both GLSQ and UMC-G approaches.