Because when Tyrion hurts you he makes sure your psychotic son who has ultimate power is as thoroughly protected and well fortified as possible while not risking his neck trying to keep Joffrey from stupidly risking his. He also sends your daughter away from the approaching army led by a man who’s family is notorious for smashing the heads of the babies of the last family of rulers they deposed. The family they deposed from the very same city and castle you are currently living in. Tyrion will viciously send your daughter to Dorn, a place that is at the moment the safest, most isolated and defensible place in all of Westeros.
When Cersei hurts you, on the other hand…she’ll have an innocent prostitute that she thinks you really care about kidnapped and beaten up. And threaten to torture and kill her with obvious enjoyment.