Sandwich structures with honeycomb cores are widely used in several applications given their promising properties, like high strength, light weight, and specific stiffness. However, these unique structures present complex behavior with failure modes that are not trivial when subjected to different loading conditions. Evaluation studies about the structural performance and failure modes of honeycomb sandwich structures with different face sheets and cores in static and dynamic conditions are scarce. Therefore, the structural behavior and failure modes of different honeycomb sandwich structures need to be evaluated to promote optimal performance in accordance with project requirements. This study seeks to characterize the structural behavior of different sandwich structures with honeycomb cores using a complete experimental comparative study. First, combinations of different types of cores and face sheets were elaborated using the Design of Experiments Method with Factorial Design, and then both the static and dynamic experimental tests were performed to obtain response variables and failure modes. The results showed that a polypropylene core in sandwich structures can increase damping. The sandwich structures manufactured with glass/aramid hybrid fabrics on the face sheets showed high strength under bending and buckling conditions, supporting a maximum bending loading of 1989 N and a maximum buckling loading of 12,700 N. Most sandwich structures had failure modes in “semi-circle” shapes. Only sandwich structures with glass fabric face sheets have failure modes in “V” shapes. Lastly, statistical results revealed that the type of core design variable contributed more to the response variability and was responsible for significantly changing the properties of stiffness, structural mass, and damping.