How do you know whether to believe his side or hers?

Put it this way, unless you were there to see or hear the situation with your own eyes or ears, then you are going to get their individual versions and have to pick which one sounds more logical or honest, which is still hard to do. I would say that you should not be asked to pick a side or choose who is telling the true version, let them hash it out and stay out of it because if you pick one, the other will get ticked and visa versa. You can see if anyone else was there and ask a neutral party, that's up to you.

ANSWER:

You can not and the best solution for you is do not take side so that way it will not come back to you and bite you in the butt.