Motility endows microorganisms with the ability to swim to nutrient-rich environments, but many species are sessile. Existing hydrodynamic arguments in support of either strategy, to swim or to attach and generate feeding currents, are often built on a limited set of experimental or modeling assumptions. Here, to assess the hydrodynamics of these "swim" or "stay" strategies, we propose a comprehensive methodology that combines mechanistic modeling with a survey of published shape and flow data in ciliates. Model predictions and empirical observations show small variations in feeding rates in favor of either motile or sessile cells. Case-specific variations notwithstanding, our overarching analysis shows that flow physics imposes no constraint on the feeding rates that are achievable by the swimming versus sessile strategies – they can both be equally competitive in transporting nutrients and wastes to and from the cell surface within flow regimes typically experienced by ciliates. Our findings help resolve a long-standing dilemma of which strategy is hydrodynamically optimal and explain patterns occurring in natural communities that alternate between free swimming and temporary attachments. Importantly, our findings indicate that the evolutionary pressures that shaped these strategies acted in concert with, not against, flow physics.