This paper analyzes trajectory observations from vehicles driving in platoon formation and they are equipped with Adaptive Cruise Control (ACC) and Cooperative Adaptive Cruise Control (CACC) systems; aiming to quantify response delays. When a preceding vehicle induces a perturbation, the delay until the reaction of the following vehicle, often quoted as observable response time, can have negative implication to the traffic flow and other factors such as energy consumption, stability and safety. Quantifying such delays can help towards more realistic traffic simulation modeling. The analysis is performed based on empirical observations from three well-known experimental campaigns in the literature with data from ACC-driven and CACC-driven vehicle platoons. Three state-of-the-art techniques were implemented to provide quantitative results for the observed response times. The benefits and downsides of each technique are discussed as well. The results show that ACC systems do not exhibit a significant improvement compared to human drivers, yet, it can be concluded that the additional vehicle-to-vehicle communication incorporated in the CACC systems allows for a substantially higher traffic flow and possibly other benefits.