When individuals store resources acquired while moving through a spatially variable habitat, a form of population structure arises. The theoretical consequences of this process for resource competition are studied for phytoplankton species consuming a single nutrient resource, using a Lagrangian modeling approach. Each competitor population is divided into many subpopulations that move through two model habitats with gradients in nutrient availability: an unstirred chemostat and a partially mixed water column. The results provide little indication that resource storage contributes to competitive fitness in the scenarios analyzed. Superior competitors usually reduce the limiting nutrient to low concentrations at steady state or sometimes have high maximal growth rates. Resource storage enhances competitive fitness in temporally variable habitats where encounters with rich nutrient pulses are strongly periodic. However, in purely spatially variable habitats where encounters with rich nutrient patches are random, resource storage does not appear to provide much benefit, at least for passively moving organisms that cannot control their location.