Why do people still bring up the Itachi hype. As he was working as a covert op and is a known liar his statement is to be taken with a grain of salt.
Realistically, Jiraiya loses this fight.
They have both long range and short range attacks in addition to being able to fuse every element.
Furthermore Jiraiya has no way to get past Diamond Skin. He might be able to do so with Oodama Rasengan but that requires he move in close at which point Hidan could scracth him, he could be caught with the earth release tentacles or the jutsu could have no effect.
Jiraiya won't get the time to go Sage Mode unless his summons stall for him but they'll die in the process (Though the Giant Toads' swords might be handy) After that the only thing Jiraiya could maybe use is Pa's Fighting Tongue Slash
But Jiraiya is a bad match up. He's more powerful in general but the match up here for him is unfortunate.