You need to stay out of it. When you talk with each of them, be sure you express to them that you will refuse to talk about the subject or the other friend.
My friend has gone through a bad breakup, she's really upset and I have been talking to the guy she broke up with too. She wants closure, and he doesn't feel ready to talk about it yet. I'm trying to help them both and I don't know what to do anymore?
Sometimes the best thing you can do in these type of situations is do absolute nothing. The next best thing is to do is just listen and offer no advice. Unless you have classroom training or life experience here, youre going to make a huge fool out of yourself and/or make things worse. Time will take care of this so just easily bow out and let Nature solve this one