In literature, priority-controlled and right-hand priority intersections have rarely been compared on other elements than the number of right-of-way violations and collisions. This study investigates the effect on speed and lateral position of five priority rules under two visibility conditions at an intersection (without hierarchy between branches), which is, at this moment, a knowledge gap. Fifty participants drove five different routes in a simulator and were exposed to the following manipulations: priority to the right rule applying and indicated (road sign and road sign with road marking), priority to the right rule applying but not indicated (no sign), priority to the right rule not applying and indicated (priority road and priority at next intersection), under good and bad visibility. Results show a significant speed decrease for both situations where the priority to the right rule was indicated compared to situations with no priority to the right rule, especially when visibility was bad. Priority to the right signs with additional road marking resulted in lowest speed under both visibility conditions. For all priority rules, lateral position shifted more towards the middle of the road when visibility was bad. Since speed was higher in case of priority roads or roads with priority at next intersection, it can be concluded that a higher level of control (priority-controlled intersections) does not necessarily result in a traffic safety improvement. Therefore, policy makers should take into account the results of this study and not generally change all the priority to the right intersections by priority-controlled intersections.