In order to investigate the relationship between the bonding nature and the cooperative relaxation, a comparative study of the relaxation behavior in polymeric and metallic glass forming systems has been performed based on the Bond Strength–Coordination Number Fluctuation (BSCNF) model developed by the authors. In the present work, we studied the correlations between the fragility m, the Vogel temperature T0, the degree of molecular cooperativity NB, and the Kohlrausch exponent βKWW. The results show that T0 and NB increase, whereas βKWW decreases systematically with the increase of m. Reflecting the difference of the interatomic interactions of the materials considered, the analysis by the present study reveals that the value of NB in ion-conducing polymers is about 5 times larger than that in metallic systems, and for each system, the material dependence of βKWW is clearly seen in the fragility index m and the cooperativity NB.