I do believe Jiraiya wins, but Kakashi is being underestimated.
Jiraiya.
He took out 3 paths of pein. Kakashi struggled on 1, although it was the strongest one of all but still.
Misconception.
Things didn't get complicated for Kakashi until Demon Realm jumped in. He figured out God Realm's abilities completely on his own even with Demon Realm fighting him as well. Kakashi was already preparing to kill both of them when Chouji and Chouza jumped in. He had a Raibushin ensnare Demon Realm, and was hiding in rubble with a Raikiri. And this was just after God Realm used Banshou Tenin, meaning God Realm would have been unable to dodge Kakashi's attack with Shinra Tensei. Not only this, but Kakashi was not within their field of vision. Meaning they had no way of detecting Kakashi's location, or being aware of when and how Kakashi would attack. In fact, Chouji and Chouza's arrival actually hindered Kakashi. Because they jumped in when they did, Kakashi was forced to cancel his strategy, and both Realm's survived their attack anyway, making their surprise attack futile. He was doing fine before Choji and his dad arrived.
No.
Sm Jiraiya with mid difficulty. Believe me when i say jiraiya wouldnt have it easy.
Kakashi isnt a pushover
Mid- possibly high difficulty sounds about right.
Kakashi can hold his own in base against Jiraiya, and potentially outsmart him wih a bunshin feint....Not to mention Sharingan also gives him a decent advantage as far as reactions go.
I believe Jiraiya gets the advantage when he decides to summon, Kakashi has no real counter to it...so he needs to try win before big toad is summoned.
Now if this thread is saying that Jiraiya starts in SM and Kakashi is allowed to use his MS straight away? Kakashi would win, since Jiraiya has no counter to it...but I think the OP meant they start in base and only have access to those abilities.
So yeah, Jiraiya does win this most of the time...but by no means will it be an easy fight.