If your answer is "Of course Olympians will win" then you should read this to find why it's wrong:
All of the pictures belongs to their respective owners
Now before going about their stats or abilities, we should start with their titles, especially for Olympians;
Titles like 'Gods' mean absolutely nothing because they are very broad terms. Fiction has omnipotent Gods like TOAA from Marvel and it also has gods like Yato from the anime Noragami, who can't even destroy cities. So what we shoul be looking is their feats.
Percy Jackson Gods are immortal but not invincible. Typhon incapacitated Zeus by stealing his sinews. So they can be defeated.
STATS
We will look at their raw stats like Destructive Capacity, Durability or Speed. In most cases an overwhelming stat difference can end a fight without starting even if the other side has a wonderful special ability. A much faster character can kill his opponent in milliseconds or someone with massive firepower can destroy whole area etc.
Destructive Capacity
This is the amount of damage a character can produce. There is also the term Attack Potency which used for the characters who don't have big destruction feats but can hurt someone with high durability.
Example: If character A can hurt Superman by punching him, then A will have a high Attack Potency even if A didn't even destroy a building.
Naruto
His most powerful attack isn't very clear destruction wise because it happened at above clouds and we also didn't see how much area it covered in that scan but here is his other attack:
Tailed Beast Rasenshuriken: An attack that he can spam. He and all his clones can use several of them at same time. Here it is:
These meteors were big:
Just the debris from them dwarfed entire mountain ranges
So he can spam an attack that a single one of them can engulf and destroy a huge meteor which was big enough that just debris of it dwarfed mountain ranges. Also together 6 of TBRS destroyed meteors that were created from a small country.
And here feats from Boruto:
Olympians
Gods in Percy Jackson don't have much feats in modern times. Their main feats come from ancient times where they fought with Titans though they also did some things in modern times:
- The most powerful feat used in war between Gods and Titans is done by Zeus. He used his Master Bolt and sheared top of a mountain. In another time he used multiple times to raze a city. Master Bolt described as the most powerful weapon ever created.
Which comes short of even smaller Tailed Beast Bombs.
- Zeus flooded entire world at one time. This is the biggest destruction he caused to humans. But although it can drown millions of normal humans, it can do nothing against strong opponents like other gods.
Not to mention even fodder level ninjas can walk on top of water.
Zeus can lift a mountain and Poseidon can hurl part of an island to large distances. Which means strength wise they are well above Naruto who can lift several hundred tons of stone in his Sage Mode.
They can also lift the sky but this isn't a physical feat because it's clearly stated in book that it's related to strength of the heart. Otherwise it would be illogical considering beings with vast strength difference all resisted it barely. And the atmosphere equals to roughly 2000 Everest which would mean Annabeth could lift mountains with her pinky which isn't the case.
Lastly, things like Sun Chariot being the Sun or creating constellations aren't in literal meaning. The Sun Chariot isn't the Sun itself, it's stated by Apollo. The real Sun is still stays in space and there are more than one sun god. Which means Apollo driving chariot isn't same as moving the Sun.
Durability
The amount of damage they can tank.
Naruto
By far his most impressive durability feat is resisting a beam that cut the moon into two halves with his inferior chakra cloak.
Olympians
Their durability isn't very clear. While they sometimes defeated by demigods, most of these times they can't use their full power because of restrictions. Still considering Master Bolt is a threat for them, their durability is well below Naruto.
Speed
Naruto
His best speed feat also happened in gifs above. Toneri's beam travels very fast. It grew large enough to bisect the moon in at most 7 seconds, when watching the scene in slow motion, it's even faster.
Toneri fired the second beam at Naruto after he started running to Toneri. Naruto ran 6 seconds before the beam reached him and 10 seconds after it. Which means he has around 0.6x of the beam's speed and that would put him around at Mach 875 in low end calculation.
Also this feat happened in his base form. His chakra cloaks boost his speed massively.
Olympians
They have supersonic feats but how faster they are is unquantifiable. By scaling from demigods -since they can match some serious gods- they are definitely not above high double digit Mach since Percy's best speed feats aren't that high and he is considered as strongest (and also one of the fastest) demigod.
Also they have teleportation.
Hax
Both sides have many special abilities, I will only write some of the 'Hax' abilities which will be the ones that can ignore durability and need special kind of counter. You can read their other techniques in Naruto's or Olympians' wiki.
Naruto
He had a very powerful hax called Truth-Seeking Balls but he lost them after the fight with Sasuke. So now his only ability that can barely called a hax is his rasenshuriken and it's variations.
The one he uses most can cut at cellular level.
Olympians
They have wide range of abilities and some of them are hax. One of the most useful one in a fight would be Transfiguration.
But this too has a weakness: it can't be used against powerful opponents otherwise fights with other gods or Typhon would end the moment it started. They can use this against other gods in myths but not when they are equal to user or stronger then them.
And here, detailed version which I wrote in another forum:
HAX
This part will be just my theory because books didn't explained it but i will give evidences. I read wiki again and Medusa wasn't only divinity got cursed.
Before starting a little info: Oceanids are daughters of titans Oceanus and Tethys(there are 3000 Oceanids) and they are goddesses.
Some famous ones: Metis(Zeus' first wife), Eurynome(Zeus' third wife), Perseis(wife of Helios and mother of Circe), Klymene(mother of Atlas) etc.
And nymphs are also considered minor goddesses in Riordanverse.
Now let's continue:Gods can also curse other gods:
-Hades had an affair with a nymph named Minthe and angry Persephone transformed her to a plant called mint.
-Again Hades fell in love with an Oceanid named Leuke but forced to transform her into a poplar tree due to Persephone's jealousy.
-Athena transformed and cursed Medusa, daughter of Keto and Phorcys(children of Gaea and both of them are gods).In every one of them, cursing side is stronger than other. Divinity isn't important here, power is the important thing. Remember when opponents are strong, like Typhon or Kronos, they couldn't curse them.
But there's an exception here: even though Big Three have comparable powers, Zeus can take their divine powers or make them mortal for punishment. But it's because he is their god king and he has authority over them.
Conclusion
In my opinion, even if we don't restrict their true forms or hax abilities, it won't affect Naruto.
It will be like fighting against Typhon. They can't affect him so they will have to fight directly.
Also if we go into divinity, Naruto also has chakra of 9 parts of Shinju, divine being.
Conclusion
Olympians have massive physical strength advantage. But they need to get close range for this to be useful which will be difficult because of speed difference. Naruto also fought people with instant teleport and his Sage Mode gives him passive prediction for these kind of situations.
Olympians would have hax advantage if not for Naruto being this powerful. Their Transfiguration or other special abilities don't work on stronger beings. If it comes to divinity clash, Naruto has 9 parts of a primordial being in his universe (Shinju).
Master Bolt, most powerful weapon from Olympians' side is weaker than normal Tailed Beast Bombs and even Naruto's clones can spam much stronger versions.
Naruto's cloak can tank everything they throw considering nothing in Riordanverse is even close to a beam that cut the moon.
Basically Naruto outstats them in every category except physical strength which would be useless because of speed difference and they also can't use their Transfiguration because of power difference again.
So winner would be Naruto in both In Character and Bloodlusted state.
But please remember this is the Riordanverse Olympians and they are much weaker compared to other myth versions. While these gods have very good feats outside of battle, like creation; they are nothing like original ones that can fight star sized opponents. If this versus was between Naruto and Mythology Gods, it would be stomp with just one of the weaker gods.
Thanks for reading. If you want another thread like this, you can reply for who do you want to see in versus.
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PS: Posts can be a little slow since I write everything from my phone because I don't have a PC so bear with me please.
And if anyone is wondering, if this versus is random; it isn't. I am an avid fanfiction reader and Naruto&Percy Jackson has one of the most crossover fanfictions. But most of the writers think Gods are well above Naruto and this made me write this post...