Anxiety/obsessive-compulsive disorders are common among youth with autism spectrum disorder (ASD). Two versions of cognitive behavior therapy (CBT) are effective, with some advantage for a personalized, adapted version. This study evaluated predictors and moderators of standard CBT and adapted CBT. Youth (N = 167) ages 7-13 were randomized to standard or adapted CBT, or treatment-as-usual. Age, IQ, ASD severity, and emotional-behavioral symptom severity were examined. More severe internalizing and emotional-behavioral problems predicted poorer treatment outcomes especially in standard versus personalized CBT. Elevated repetitive behaviors and restricted interests predicted poorer treatment outcomes across treatments, though youth with "moderate" repetitive behaviors and restricted interested experienced poorer outcomes only in standard but not personalized CBT. Externalizing symptoms directly predicted treatment outcomes. Older age predicted improved outcomes in adapted but not standard CBT. Findings highlight the need for further treatment refinements and the value in adapting treatment for youth with more complex presentations.