Leebrucea I will go through everything you just talked about:
Note: You can't predict or go by the databook to conclude a battle.
Ninjutsu:
Jiraiya: Doton/Katon He has mastered these elements to such perfection, that at just 30 % strength, he is capable of creating a swamp big enough to sink Manda and other snakes at once. His Fire release is also impressive, capable of taking out a single animal with a single offensive. Also his Jutsu varies in size and area affected. If we include his ninjutsu as in Rasengan and hair jutsu it is greatly increasing his abilities as he is shown to be able to defend against almost anything and that the Rasengan is surperior to lightning release.
Kakashi: Raiton/Suiton He also has over 1000 jutsus copied with his Sharingan. Though his main element is shown to be lightning and he is well rounded in Doton and Suiton, though Jiraiya far surpasses Kakashi with his Doton and can protect against suiton with it, also his suiton is impressive but Jiraiya's fire release combined with oil would defeat it too.
- Jiraiya is surperior when it comes to Ninjutsu terms -
Taijutsu:
They both have 4.5 for taijutsu, in the last databook, though as we have seen they are both incredible skilled when it comes to that field. Kakashi has shown great feats in all his battles and his Sharingan gives him a whole other edge to fight an opponent.
Jiraiya on the other hand, his Taijutsu is impressive and he has shown little in that field, though but he has managed well against many opponents and as shown in a few flashbacks and fights he has been in he has shown surperior in that field.
- Kakashi is surperior in Taijutsu because of his Sharingan, BUT if Jiraiya is capable of entering Sage Mode, then Jiraiya far surpasses Kakashi -
Speed:
In this field they both have the same in the databook, though yes Kakashi has improved, but in the same way Kakashi will have incredible trouble in facing Jiraiya since Jiraiya is quite fast, and especially if he enters Sage Mode he exceeds Kakashi by far, as shown when he jumps off a wall while creating a massive rasengan and striking one of Peins bodies before his sandals even touch the ground.
- Jiraiya & Kakashi is about equal when it comes to Speed, but if we go to Jiraiya in Sage Mode, Kakashi is then far surpassed yet again -
Strength:
Jiraiya: Jiraiya has incredible strength even without Sage Mode, but if he enters Sage Mode, his strength will be so immense he can deliver a single punch which would probably crush the skull and several bones with ease... this is shown in the manga as he takes down one pein with a single blow.
Kakashi: He is quite strong, and as of now we only know that he can entr 1 gate, so that is what we go for, and Kakashi without opening a gate will fall to a normal Jiraiya, if he enters a Gate he will be able to fight Jiraiya head on and possible win, unless Jiraiya enters Sage Mode.
- Jiraiya surpasses him in strength -
Jiraiya > Kakashi
Jiraiya < = Kakashi 1st Gate
Jiraiya SM > Kakashi 1st Gate
Intelligence: This field I'm surprised you said Kakashi, I mean Jiraiya made so many strategies and defeated many opponents with ease and he crushed several summons and held of Itachi & Kisame (debatable) and he went head on with Pein and his strategy of a defensive move a along while fighting down 4 animals and finally coming up to Sage Mode and crushing several of Peins paths. While he was waiting for Sage Mode he never revealed himself to his opponent it was all a set of clones.
Jiraiya managed all this with no intelligence at all about his enemy, while Kakashi did worse against same level of opponents, though he had some intelligence on them.
- In this field Jiraiya is above Kakashi by far as shown in the manga even though Kakashi is smart -
Stamina:
Kakashi stated it himself, he does not posses much stamina even though he improved alot, Jiraiya has an immense amount of chakra/stamina and surpasses him in this field.
Genjutsu:
Here Kakashi has the Sharingan and is quite skilled in Genjutsu as Jiraiya is not, but Jiraiya has Ma & Pa to support in that Area if entering Sage Mode, and there their song genjutsu is arguably one of the strongest Genjutsu's in Naruto, and even though you have sharingan does not mean you wont be able to fall for it.
- Kakashi is surperior in this field, unless Jiraiya has Ma & Pa -
Summoning:
Kakashi has Dogs, Jiraiya has Toads, and we have obvious reasons to believe that the Toads are far surperior than that of the dogs, because of their giant bosses and their abilities.
- Jiraiya obviously has the best summons -
Conclusion: I know i left out a good explanation to much of Jiraiya's abilities, but Sage Mode amplifies Speed, Strength, and his Ninjutsu is greatly increased and gives him a whole new arsenal to use. Also Jiraiya in Sage Mode gives him a sensory type ability to sense an opponent before they strike, that will be a good counter to Kakashi's sharingan, and in Sage Mode Jiraiya will be unable to be caught in Genjutsu because of Ma & Pa and Natural Energy. Also I wanted to state that Jiraiya has never been caught in a Genjutsu... never shown in Manga or Anime.
- Jiraiya wins this with Mid difficulty at best -