Robotics is tightly connected to both artificial intelligence (AI) and control theory. Both AI and control based robotics are active and successful research areas, but research is often conducted by well separated communities. In this paper, we compare the two approaches in a case study for the design of a robot that should move its arm towards an object with the help of camera data. The control based approach is a modelfree version of Image Based Visual Servoing (IBVS), which is based on mathematical modeling of the sensing and motion task. The AI approach, here denoted Behavior-Based Visual Servoing (BBVS), contains elements that are biologically plausible and inspired by schema-theory. We show how the two approaches lead to very similar solutions, even identical given a few simplifying assumptions. This similarity is shown both analytically and numerically. However, in a simple picking task with a 3 DoF robot arm, BBVS shows significantly higher performance than the IBVS approach, partly because it contains more manually tuned parameters. While the results obviously do not apply to all tasks and solutions, it illustrates both strengths and weaknesses with both approaches, and how they are tightly connected and share many similarities despite very different starting points and methodologies.