What is mind break in this instance? Usually it involves drugs, magic or extreme violence and it doesn't matter who the person was before, you're breaking her mind anyway. You can't mind break someone by just talking or blackmailing.
If you mean just making her to change her mind and ditch her LI\become slut, then tsundere is obviously easier, since she's just a normal girl playing hard to get basically. Jealousy is the obvious way, since tsundere is convinced her target is head over heels for her and seeing otherwise would plant a lot of doubts in her head and can force some desperate uncalculated decisions you can exploit.
Yandere is an obsessed fanatic, so that should be way harder, as with any fanatics. I would play into her obsession. Maybe get friendly with the guy first, then tell her you will help to get to your friend because you want him to be happy and make her do some crazy shit. And when that guy starts hating her say that it's all her fault since she failed to do it right, but there's this one thing that can save everything... And after a while she can actually go crazy for good
But that may not end up well, yandere and all.