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Dawn is stronger than Ash. She captured Dialga, Palkia, Giratina, Regigas. She became champion and shut down team galactic on her own. She's so strong that Paul never even appeared on her radar, and neither did Ash, both were weaklings who weren't even strong enough to appear as random trainers on a random route.
But the chuuni executive nerfed her so she could be his self insert's submissive wife.