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Both rotation and interactions with binary companions can significantly affect massive star evolution, altering interior and surface abundances, mass loss rates and mechanisms, observed temperatures and luminosities, and their ultimate core-collapse fates. The Geneva and BPASS stellar evolution codes include detailed treatments of rotation and binary evolutionary effects, respectively, and can illustrate the impact of these phenomena on massive stars and stellar populations. However, a direct comparison of these two widely-used codes is vital if we hope to use their predictions for interpreting observations. In particular, rotating and binary models will predict different young stellar populations, impacting the outputs of stellar population synthesis (SPS) and the resulting interpretation of large massive star samples based on commonly-used tools such as star count ratios. Here we compare the Geneva and BPASS evolutionary models, using an interpolated SPS scheme introduced in our previous work and a novel Bayesian framework to present the first in-depth direct comparison of massive stellar populations produced from single, rotating, and binary non-rotating evolution models. We calculate both models' predicted values of star count ratios and compare the results to observations of massive stars in Westerlund 1, $h + χ$ Persei, and both Magellanic Clouds. We also consider the limitations of both the observations and the models, and how to quantitatively include observational completeness limits in SPS models. We demonstrate that the methods presented here, when combined with robust stellar evolutionary models, offer a potential means of estimating the physical properties of massive stars in large stellar populations.