I'm amazed at how crazy people can get when they say Itachi will win or Jiraiya will win. Instead of posting more reasons to support my opinion I will ask some questions.
1.Do you think Itachi would have told Kisame the truth when he said Jiraiya was stronger?
2.How do you beat an invulnerable shield? (and sealing sword)
3.How good do you think Jiraiya is at Genjutsu?
he stated himself its his weakpoint thats why pain would never expect him to use it.
4.If he said that fighting a Sharingan user one on one, you should run away. Would he follow his own advice?
5.If Jiraiya did follow Itachis feet so he wouldn't look into his eyes like Gai. Do you think that he would be able to fight better?
6.If you are watching Itachis feet. What about his Shadow Clone?
7.If you were caught in Tsukuyomi, is that Game Over for Jiraiya?
Depends on how painful itachi makes it, he could have killed kakashi with it so probably could kill jiraiya
8.Would there be a way to overcome the sound genjutsu of Ma and Pa?
9.Wasn't Itachi a amazing taijutsu and ninjutsu user. Now he is a master of genjutsu too?
genjutsu was always what hes best at, hes excellent overall but noones better in genjutsu then itachi.
10.Wasn't Jiraiya a noob at genjutsu?
11.Wasn't Itachi really clever and Jiraiya a bit dopey?
I am not going to point out all the characters Itachi and Jiraiya could have beaten up. As I said in another post. Ninjas have a rock, paper scissor system. One can beat another but get ripped up by another weaker ninja.