To explore and compare the failure modes, deformation behaviors, and load-bearing capacities of single-edge notched (SEN) beams strengthened with carbon fiber-reinforced polymer (CFRP) and steel bars, static and dynamic three-point bending tests on both types of concrete beams have been carried out in this study. During the static tests, the electro-hydraulic servo machine served as a loading device to apply pressure to CFRP beams and reinforced concrete (RC) beams. During the impact experiments, different impact velocities were imparted by adjusting the drop hammer’s height. Thus, information regarding crack propagation, energy absorption, and deformation was obtained. The results from the static tests showed that the RC beams predominantly experienced shear failure. In contrast, the CFRP beams primarily exhibited bending–shear failure, attributed to the relatively weaker bond strength between the bars and the concrete. Impact tests were conducted at three different velocities in this study. As the impact velocity increased, both types of concrete beams transitioned from bending failure to bending–shear failure. At the lowest velocity, the difference in energy absorption between beams reinforced with different materials was insignificant during the bending process. However, at the highest velocity, CFRP beams absorbed less energy than RC beams. The study of structures’ impact failure modes and their mechanical characteristics offers valuable references for the anti-collision design and protection of structures.