To investigate the influence of crosslinking methods on the releasing performance of hybrid hydrogels, we synthesized two systems consisting of Graphene oxide (GO) as a functional element and alginate as polymer counterpart by means of ionic gelation (physical method, HA−GOP) and radical polymerization (chemical method, HA−GOC). Formulations were optimized to maximize the GO content (2.0 and 1.15% for HA−GOP and HA−GOC, respectively) and Curcumin (CUR) was loaded as a model drug at 2.5, 5.0, and 7.5% (by weight). The physico-chemical characterization confirmed the homogeneous incorporation of GO within the polymer network and the enhanced thermal stability of hybrid vs. blank hydrogels. The determination of swelling profiles showed a higher swelling degree for HA−GOC and a marked pH responsivity due to the COOH functionalities. Moreover, the application of external voltages modified the water affinity of HA−GOC, while they accelerated the degradation of HA−GOP due to the disruption of the crosslinking points and the partial dissolution of alginate. The evaluation of release profiles, extensively analysed by the application of semi-empirical mathematical models, showed a sustained release from hybrid hydrogels, and the possibility to modulate the releasing amount and rate by electro-stimulation of HA−GOC.