Many researchers argue, in assessing the benefits of Advanced Driver Assistance Systems (ADAS) it has to be taken into account that any gains in terms of security may be again reduced by the fact they affect the drivers' behavior. In this paper, we present results of a driving simulation study in which we compare driving performance as well as driver stress in three conditions: 1) when no assistance is available (NOASSIST) ; 2) when the system is working as it should (WORK); 3) when the system suddenly fails (FAIL). Results show that the driving performance is severely affected by system failures. The drivers' ability to effectively react to suddenly appearing obstacles FAIL is significantly lower than in NOASSIST. At the same time, the stress level is significantly higher in FAIL compared to WORK.