Previous research has shown that chimpanzees exploit the behavior of humans and conspecifics more readily in a competitive than a cooperative context. However, it is unknown whether bonobos, who outperform chimpanzees in some cooperative tasks, also show greater cognitive flexibility in competitive contexts. Here we tested the cooperative-competitive hypothesis further by comparing bonobos and chimpanzees in a series of tasks where a human gesture indicated the correct (cooperative) or incorrect (competitive) choice. A human either pointed cooperatively to the object a subject should choose, or competitively to the object subjects should avoid choosing. In contrast to previous research, subjects were most skilled at choosing the correct location when the communicator was cooperative and there were no major differences between bonobos and chimpanzees. Analysis of gaze direction revealed that in some cases subjects visually followed the direction of the experimenter’s gesture despite choosing incorrectly, dissociating gesture following from gesture comprehension. This supports the hypothesis that, unlike human children, nonhuman apes respond to the direction of social gestures more readily than they understand the communicative intentions underlying them. We evaluate these findings in regard to previous studies comparing the cooperative and communicative skills of bonobos and chimpanzees.