Aura hypnosis ability is based on mana, she just compares her mana power to her opponent, and the weaker one loses all free will. Frieren is one of the most powerful wizard in the world... so she got cocky, but she didn't know Aura had another ability:
“Riki and Kunio? Those losers? Just let the magic fry those sweet dumb brains, girls. Then you’ll find I’m more than enough to replace them both.” (River City Girls | Kyoko & Misako x Yamada | Merunyaa)