Skilled motor behavior relies on the ability to control the body and to predict the sensory consequences of this control. While there is ample evidence that manual dexterity depends on handedness, it remains unclear whether control and prediction are similarly impacted. To address this issue, right-handed human participants performed two tasks either with the right or the left hand. In the first task, participants had to move a cursor with their hand so as to track a target that followed a quasi-random trajectory. This hand tracking task allowed testing the ability to control the hand along an imposed trajectory. In the second task, participants had to track with their eyes a target that was self-moved through voluntary hand motion. This eye tracking task allowed testing the ability to predict the visual consequences of hand movements. As expected, results showed that hand tracking was more accurate with the right hand than with the left hand. In contrast, eye tracking was similar in terms of spatial and temporal gaze attributes whether the target was moved by the right or the left hand. While these results extend previous evidence for different levels of control by the two hands, they show that the ability to predict the visual consequences of self-generated actions does not depend on handedness. We propose that the greater dexterity exhibited by the dominant hand in many motor tasks stems from advantages in control, not in prediction. Finally these findings support the notion that prediction and control are distinct processes.