Suggested by iKnowledge Jean Grey is a very skilled telepath whose experience with the Phoenix also gave her some real combat abilities. While she probably couldn’t do much to Joker’s mind, she won’t even need too. Joker won’t really be able to defend himself from her physical attacks. He is completely helpless against the Phoenix Force and its unrelenting fire strikes. His best hope would be to trick Jean Grey into looking at his mind, but she is too smart for that. Jean Grey wins.
DReager1.com 
I agree with you here, Dreager1. Although I think the Phoenix is powerful enough to turn the Joker sane. And when he becomes sane….He’ll beg to be burnt by the Phoenix, so great would be his remorse, as demonstrated by these scans: http://i.imgur.com/3lJKOKH.jpg, and https://lowbrowcomics.files.wordpress.com/2016/03/batman-legends-of-the-dark-knight-145-2001-digital-empire-010.jpg, as well as this: https://lowbrowcomics.files.wordpress.com/2016/03/batman-legends-of-the-dark-knight-145-2001-digital-empire-012.jpg.
Definitely some interesting scenes for the Joker there. It almost doesn’t seem in character for him to be sane at all, but the Phoenix is an incredible telepath so you never know I suppose. Breaking the Joker would be quite the feat!