Perfect SM Jiraiya: No appearance flaws, can use SM Like Naruo, has Ma & Pa, has all Toads, can use Rasengan to as well as he can, everything else he has.
Hashirama Senju: At Full Hokage Mode, has all his Wood Ninjutsu, is as Strong as he was against Madara, also is equally proficient with Suiton and Doton, has his Genjutsu, and can summon Nine Tails.
I think Hashirama will barely win, because his Wood will be destroyed, but he can cancel Jiraiya's Fire Moves. Nine Tails can be beaten by the Toads. But Mokuton: Navity of a World, can be destroyed by Rasengan, but Its Sheer Size can only be stopped by Many Giant Rasengans, so Jiraiya will need to use about Three Gigantic Rasengans, to win, and that's his Ultimate Move. So I believe Hashirama will win.
Hashirama Senju: At Full Hokage Mode, has all his Wood Ninjutsu, is as Strong as he was against Madara, also is equally proficient with Suiton and Doton, has his Genjutsu, and can summon Nine Tails.
I think Hashirama will barely win, because his Wood will be destroyed, but he can cancel Jiraiya's Fire Moves. Nine Tails can be beaten by the Toads. But Mokuton: Navity of a World, can be destroyed by Rasengan, but Its Sheer Size can only be stopped by Many Giant Rasengans, so Jiraiya will need to use about Three Gigantic Rasengans, to win, and that's his Ultimate Move. So I believe Hashirama will win.