(1) Background: Inhibitory and rewarding processes that mediate attentional biases to addiction-related cues may slightly differ between patients suffering from alcohol use (AUD) or gambling (GD) disorder. (2) Methods: 23 AUD inpatients, 19 GD patients, and 22 healthy controls performed four separate Go/NoGo tasks, in, respectively, an alcohol, gambling, food, and neutral long-lasting cueing context during the recording of event-related potentials (ERPs). (3) Results: AUD patients showed a poorer inhibitory performance than controls (slower response latencies, lower N2d, and delayed P3d components). In addition, AUD patients showed a preserved inhibitory performance in the alcohol-related context (but a more disrupted one in the food-related context), while GD patients showed a specific inhibitory deficit in the game-related context, both indexed by N2d amplitude modulations. (4) Conclusions: Despite sharing common addiction-related mechanisms, AUD and GD patients showed different patterns of response to (non-)rewarding cues that should be taken into account in the therapeutic context.