Well, Tsunade has a HUGE advantage here, she has full intel while Pain has none, Chibaku is restricted, he's trying to capture her and she's trying to kill him, and since you said Pain instead of Nagato I'm assuming we're talking about the 6pop, not Nagato himself, right ?
Anyhow, under these circumstances, it could go either way. Tsunade is not a ninja you should underrate. However, I believe Pain takes this because of these reasons:
1. Animal Path: This path should be enough to hold off Katsyuu. She may be durable and may be able to split, but she won't be able to hold her own against the multiheaded splitting dog, the bird, the rhino, and the rest of his summons. She has amazing tanking abilities, but she won't be able to defend against all of his summons at once.
2. Human Path: Tsunade's fighting style almost solely revolves around using her monstrous strength in a hand-to-hand combat. However, the Human path will remove the soul of anyone who get's in touch with it, and even if Tsunade has her healing techniques, losing a soul is not something you can cure.
These two are the main reasons I think Pain takes this. There are other things, like the fact that Pains metal rods interrupt the opponents chakra flow which would be a big problem for Tsunade considering that her monstrous strength requires very precise chakra control.
Anyway, I think the 6pop take this.
P.S. If we're talking about Nagato himself, he takes this no problem.
P.S.S. I don't quite get why Chibaku isn't allowed. Pain used it against Naruto when his goal was to capture him, why not Tsunade ?