Undesired vibrations in structures, buildings, and machines lead to reduction in the life of the system and greatly affects the safety of the occupying or operating personnel. In addition, economic and time losses could result from needed repairs or reconstruction. Many control techniques, active and passive, have been devised over the years to reduce/eliminate the vibrations in the aforementioned systems. Passive vibration control techniques are favorable over the active ones due to their simplicity, ease of implementation, cost, and power consumption. In dynamic structures, such as large buildings, passive control techniques are favored over their active counterparts. The most common types of passive control devices are tuned mass and impact dampers. The advocates of each of these devices boasts advantages of the others; however, there have been no systematic studies to compare and quantify the effectiveness of each of these types of devices as well as their suitability for specific applications. In this paper, a comparative study between the tuned mass dampers and impact dampers is conducted. A one-story structure is used to show the effectiveness of each of these devices in absorbing the vibrations of the structure. The coupled systems are modeled and simulated under free vibrations. The time responses are acquired using the same geometric parameters, excitation, and initial conditions. The comparisons are based on the settling time and amplitude decay rates of the primary system using each damper type. The numerical results show that both dampers can produce similar dampening effects if the parameters are optimized; however, correlating the dampers parameters is a challenging problem in the field of vibration and control.