This study aimed to investigate food addiction (FA) and binge-eating disorder (BED) in their association to executive dysfunctions in adults with obesity. Data on response inhibition, attention, decision-making, and impulsivity were derived from four groups of adults with obesity: obesity and FA (n = 23), obesity and BED (n = 19), obesity and FA plus BED (FA/BED, n = 23), and a body mass index-, age-, and sex-stratified control group of otherwise healthy individuals with obesity (n = 23, OB), using established computerized neuropsychological tasks. Overall, there were few group differences in neuropsychological profiles. Individuals of the FA group did not differ from the OB group regarding executive functioning. Individuals with BED presented with significantly higher variability in their reaction times and a deficient processing of feedback for performance improvement compared to individuals of the OB group. Strikingly, individuals with FA/BED did not present neuropsychological impairments, but higher levels of depression than all other groups. The results indicated the presence of a BED-specific neuropsychological profile in the obesity spectrum. The additional trait FA was not related to altered executive functioning compared to the OB or BED groups. Future research is needed to discriminate FA and BED further using food-specific tasks.