While there is accumulating evidence for the importance of the metabolic cost of information in sensory systems, how these costs are traded-off with movement when sensing is closely linked to movement is poorly understood. For example, if an animal needs to search a given amount of space beyond the range of its vision system, is it better to evolve a higher acuity visual system, or evolve a body movement system that can more rapidly move the body over that space? How is this trade-off dependent upon the three-dimensional shape of the field of sensory sensitivity (hereafter, sensorium)? How is it dependent upon sensorium mobility, either through rotation of the sensorium via muscles at the base of the sense organ (e.g., eye or pinna muscles) or neck rotation, or by whole body movement through space? Here we show that in an aquatic model system, the electric fish, a choice to swim in a more inefficient manner during prey search results in a higher prey encounter rate due to better sensory performance. The increase in prey encounter rate more than counterbalances the additional energy expended in swimming inefficiently. The reduction of swimming efficiency for improved sensing arises because positioning the sensory receptor surface to scan more space per unit time results in an increase in the area of the body pushing through the fluid, increasing wasteful body drag forces. We show that the improvement in sensory performance that occurs with the costly repositioning of the body depends upon having an elongated sensorium shape. Finally, we show that if the fish was able to reorient their sensorium independent of body movement, as fish with movable eyes can, there would be significant energy savings. This provides insight into the ubiquity of sensory organ mobility in animal design. This study exposes important links between the morphology of the sensorium, sensorium mobility, and behavioral strategy for maximally extracting energy from the environment. An infomechanical approach to complex behavior helps to elucidate how animals distribute functions across sensory systems and movement systems with their diverse energy loads.