Mice are becoming an increasingly popular model for investigating the neural substrates of visual processing and higher cognitive functions. To validate the translation of mouse visual attention and sensorimotor processing to humans, we compared their performance in the same visual task. Mice and human participants judged the orientation of a grating presented on either the right or left side in the visual field. To induce shifts of spatial attention, we varied the stimulus probability on each side. As expected, human participants showed faster RTs and a higher accuracy for the side with a higher probability, a well-established effect of visual attention. The attentional effect was only present in mice when their response was slow. Although the task demanded a judgment of grating orientation, the accuracy of the mice was strongly affected by whether the side of the stimulus corresponded to the side of the behavioral response. This stimulus–response compatibility (Simon) effect was much weaker in humans and only significant for their fastest responses. Both species exhibited a speed–accuracy trade-off in their responses, because slower responses were more accurate than faster responses. We found that mice typically respond very fast, which contributes to the stronger stimulus–response compatibility and weaker attentional effects, which were only apparent in the trials with slowest responses. Humans responded slower and had stronger attentional effects, combined with a weak influence of stimulus–response compatibility, which was only apparent in trials with fast responses. We conclude that spatial attention and stimulus–response compatibility influence the responses of humans and mice but that strategy differences between species determine the dominance of these effects.