#but yeah ive come across various debates (from years ago) where people claimed jiraiya was the strongest

[sannin-three]

Imo, the argument of "which Sannin is the strongest" misses the point of the characters and their three way deadlock

The Sannin are of course references to the characters from the Japanese folklore story, The Tale of the Gallant Jiraiya. However, they also reference the game of mushi-ken, which is basically an old variant of Rock, Paper, Scissors. In the game, Slug beats Snake, Snake beats Toad, and Toad beats Slug.

This is reflected in their interactions in canon.

Slug beats Snake

This one's easy - Tsunade famously beat up Orochimaru that one time.

Snake beats Toad

Now, some people argue that Jiraiya is more powerful than Orochimaru and would easily win if they were to fight. Most often I see people cite that Itachi easily trapped Oro in a genjutsu, but hesitated to face Jiraiya.

But power scaling is more complicated than that - if we're going to compare them fighting against other people then here's a different example:

Jiraiya nearly died trying to calm Four-Tails Naruto, while Orochimaru fought him directly and got away basically fine. And when we did see the two fight, Orochimaru easily penetrated Jiraiya's defenses.

Sure Jiraiya had been drugged not long before, but Orochimaru was arguably worse off, being tired, sickly, and not having use of her arms or chakra abilities. Orochimaru even points this out:

So while Jiraiya might be able to beat Itachi (we don't actually see it happen though so it's really just conjecture) that doesn't mean he can win against Orochimaru. After all, he's been following the snake for years but never fought/defeated them in all that time.

Toad beats Slug

Now this one could be a little controversial, but hear me out:

In terms of brute strength, Tsunade trumps both of her teammates easily; there's no question of that.

But strength isn't everything in a battle. And I think this moment says a lot:

Jiraiya states that he will kill Tsunade if she chooses to betray Konoha, and neither of them question that he has the ability to do so. So while she might regularly beat his ass when he's doing dumb shit, the implication here is that if they were to fight seriously and he genuinely wanted to hurt her, he could. Maybe not with strength alone but with technique and determination he could ultimately take her down.

Deadlock

And there you have the crux of their team - one might be able to defeat another, but no individual can beat both opponents. This is why the deadlock exists. They keep each other in check.

And this is also why they were always more powerful as a team...