I have. If the person is my family, unless they did something truly heinous, I will choose them. I won't say bad things about the other person or anything like that, but I will no longer see the ex. Wrong? Maybe. But I'm not trying to have drama.
If this is friends I will choose whomever I want to maintain a friendship with more. In a perfect world, I could stay friends with both. But, I tried that one or twice and it was unpleasant.