I actually think Doctor Strange would win.
Agatha's draining power seems to suck life force and magical ability from a magic wielder, but I'm not certain that Doctor Strange's power can be drained because he doesn't have natural magical power, but draws it from other dimensions, as explained by the Ancient One.
"We harness energy drawn from other dimensions of the multiverse to cast spells, to conjure shields and weapons, to make magic."
Wanda's magical ability seems to come from within her, as Agatha said she was a fledgling witch when she cast the probability hex on the Stark bomb as a child, hence why Agatha could drain Wanda of her power. I might be forgetting something, but technically anyone could learn the kind of magic Masters of the Mystic Arts wield. Witchcraft and sorcery may be two different schools of magic in the MCU.
It's just a theory, but I think there's plenty of evidence to suggest that Agatha can't absorb the magic Dr. Strange wields. And since there's no specific win condition, Strange could just BFR her to the mirror dimension.
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