Cursed Mode Jugo (in his ADULT FORM unlike the CHILD FORM he was in against the raikage) is stronger and faster than SM Jiraiya but he would still lose to Jman.
I don't see what Jugo can do against swamp of the underworld, though he could possibly escape it with his laser cannons by turning it into glass with the heat from his jutsu and then breaking out, since swamp of the underworld is an earth based jutsu.
Jiraiya has that oil, wind, fire combo attack with ma and pa and that fast and wide range hair jutsu but those would never work against Jugo, Jugo's laser cannons could counter both of those jutsu plus the guy has insane speed and reflexes, he was quick enough to react to the raikage's speed by not only blocking his attack with his arm but still had the time to actually turn his arm into a cursed shield to counter the punch, and that was done while he was still in child form (he turned into a child version of himself when he healed sasuke against killer bee, was still in child form at the summit because he was the shortest person there), he is probably way stronger and way faster in adult form, even C was impressed that he was keeping up with the raikage in his child form, though the raikage was only in V1 armour too.
Jiraiya would also have to be weary of close range battle, Jugo has shown the ability to absorb people into himself with a syringe like extension, if he gets too close he might risk getting absorbed.
Jugo can also increase the power of his attacks even further with his jet boosters that he grows on his elbows and arms plus the same jet boosters have been used to increase propelsion and speed in the killer bee fight, similar to how asura path uses his chakra boosters to propell himself, this would further increase his already high speed, this ability would also make it difficult for Jiraiya to avoid the suicidal close renge battle that Jugo would no doubt try to maintain.
Plus jugo can turn his limbs into any weapon he wants, or just grow a weapon on his limbs for attack and defense, this is another problem in close range, you just don't know what to expect from this guy.
This fight would be no doubt tough for Jman but I think he could win even if frog song is restricted.
Jiraiya can summon gamaken or gamabunta to distract Jugo while he prepares a trap of some sort, like the stomach barrier or toad oeso****us, or hit him with cho oadama rasengan while he is distracted with Gamabunta, probably wouldn't kill him but would weaken him enough for Jman to finish him off.
Jiraiya wins with mid difficulty, Jman has too much diversity in his jutsu arsenal and with ma and pa and other summons to call forth, he also has the numbers advantage, plus he has the intelligence advantage, Uugo maybe quite smart in base form but he is also too weak to trouble jman in his base form so he needs curse mode to have a the power and speed advantage, but that means he loses his intelligence and Jiraiya just outsmarts him, either way, Jugo will lose this battle, he would put up a good fight though I'll admit, but will lose to one of the stronger sannin.