The energy absorption behavior of crashboxes made of steel/polymer/steel (SPS) sandwich sheets can be influenced by numerous parameters, such as the materials used, their thicknesses and stacking, and the adhesion properties between their layers. Therefore, in the present study, the impact of steel/polymer adhesion quality on the occurring failure modes of the crashboxes and the resulting energy absorptions are experimentally analyzed. For this purpose, axial crushing and three-point bending tests on double-hat and top-hat crash boxes were performed, respectively. Three levels of adhesion quality are investigated: none, weak, and strong adhesion strengths. Additionally, the structural crash properties, such as energy absorption and maximal intrusion, are determined and analyzed at both of the quasi-static and highly dynamic loading rates. The results of these investigations show that the adhesion strengths chosen here significantly influence both the failure modes and the energy absorption values. In particular, the structural parameters, in the case of no adhesion, are at most half of those in the case of strong adhesion. However, it is also shown that, in the case of weak adhesion, the structural characteristics are slightly reduced. Based on these results, the possibility to adjust the adhesion strength—globally and/or locally—could be used in future activities to purposefully tailor the failure behavior of hybrid crashboxes.