Circular migrations are the periodic movement of individuals between multiple locations, observed in parts of sub-Saharan Africa. Relationships between circular migrations and HIV are complex, entailing interactions between migration frequency, partnership structure, and exposure to acute HIV infection. Mathematical modeling is a useful tool for understanding these interactions. Two modeling classes have dominated the HIV epidemiology and policy literature for the last decade: one a form of compartmental models, the other network models. We construct models from each class, using ordinary differential equations and exponential random graph models, respectively. Our analysis suggests that projected HIV prevalence is highly sensitive to the choice of modeling framework. Assuming initial equal HIV prevalence across locations, compartmental models show no association between migration frequency and HIV prevalence or incidence, while network models show that migrations at frequencies shorter than the acute HIV period predict greater HIV incidence and prevalence compared to longer migration periods. These differences are statistically significant when network models are extended to incorporate a requirement for migrant men's multiple partnerships to occur in different locations. In settings with circular migrations, commonly-used forms of compartmental models appear to miss key components of HIV epidemiology stemming from interactions of relational and viral dynamics.