Let's look at this rationally. I will be considering feats, raw power, abilities and their versatility, variable experiences, training environment, and last but not least Percy’s realistic motivations for gaining more and more power while Jason's powers stifling due to a stagnant environment, all based on the amount of information provided to us.
(I am not considering the fight op is talking about, because they were both being controlled by eidolons and the fight was prematurely interrupted and contrary to op's opinion Jason was also very biased to himself after the fight and if we are considering unreliable narrators, Piper whose pov we have for this fight is infatuated with Jason and that also counts as grounds for unreliable narration)
Percy has got Jason beat in feats before they even met, and especially after they met. Cue Tartarus. As for Jason, we know very little about the things he did and what other feats he has. We really don't have much to go off of regarding Jason's expertise in either hand to hand or power based combat but I assume everyone is leaning towards Jason in terms of hand to hand because he referenced that he fought Krios with his bare hands. Percy had wrestled with Geras, the very personification of old age who is impossible to overpower and managed to hold his own.
So the hand to hand combat is a maybe. But Jason isn't a solo fighter. Percy is, and also Percy's way better at thinking on his feet. Percy has had a very non-linear approach of learning about the demigod world and his own powers, almost all through practical experience with little traditional training. Which make his mindset towards battle superior to Jason's as Percy has no preconceived notions about domains and their limits and can actualize most things he visualizes while Jason is a bit hindered by Camp Jupiter's approach towards training for the betterment of the legion, more so than honing individual capabilities. This makes Percy terrible at teamwork and synchronized fighting as his experience lies mostly in going solo in combat while Jason is much better at the former than him.
We have also seen that Greek demigods have more volatile powers than Romans do; Thalia, Nico and Percy all show a strong innate raw power as compared to the Roman aspects as evidenced by the Gods themselves saying that their Roman aspects are much more restrained and disciplined while their Greek aspects are more wild and primal. Another canon evidence for this is how Greek demigods have such strong scents that monsters hunt them for childhood, leading to much lower life expectancy as compared to Roman demigods.
Percy has probably the most volatile as well as versatile powers. He can heal himself something Jason can't do, something no other demigod can do. Most fictional magic systems almost always associate the water attribute to healing, so it is unlikely that Jason will be able to self heal, even after unlocking his full potential.
Not to mention, Percy's abilities might not be the best[Hades children have better abilities], but in terms of raw power, no one is close to Percy. Blowing up an entire volcano, lifting an entire river off its riverbed, holding the weight of the sky, jumping an impossible distance to get to the House of Night, causing hurricanes, storms, a tidal wave so great the God of War was smothered, summoning water by will, going toe to toe with Chardybis in her own domain, and then some.
And sure, Percy seems less experienced than Jason, but he has been in more life-death situations than Jason in such a small amount of time that he had to adapt far more. Then, he has the added experience from Tartarus. And even without it, Percy gets the edge cause in mere span of 5 years of being in the demigod world, Percy has killed almost every monster that walks, fought Titan, fought minor gods and even a god. Fought and won.
Even without sea, Percy has higher raw power, more versatile abilities, and has experimented more with his powers than Jason. The latter has not even honed the lightning aspect of his powers. He has killed multiple titans, fought Kronos to a standstill, fought giants singlehandedly, fought a protegeneoi, and won against it in her own domain. That scales Percy on a level that is unattainable by any current demigod in the verse. Not even a god to our knowledge of Riordanverse has bested that feat.
I love Jason as much as the next person, and I always consider Jason to be a stronger demigod than Nico, who is generally scaled after Percy. Cause of stamina reasons. Nico’s powers are beyond exceptional, but they have limited usage time while Jason has higher stamina reserves than Nico and is a better combatant than Nico. But you can't apply this metric to Percy. Percy disarmed Luke in their first fight with little knowledge of sword techniques. Luke, who was considered the best swordsman in the last 300 years. And Luke taught Percy after that, too.
I know everyone likes to cry plot armor over Percy's powers, but technically, it is his series. There would be no point to it if he didn't get stronger. That's literally the definition of a main character. And not to mention that every time Percy gets stronger, it's always due to a strong emotional, physical trauma, or an equally terrible price that is a result of a curse/blessing. Moreover, Percy has realistic motivations to try and grow stronger since he did all he could to survive since he was 12 and was basically thrown uninitiated as a bait to the strongest monsters and was repeatedly told his birth was a mistake so much so that gods voted on whether to keep him alive. Percy has to be strong in a world where everything is out to get him. The literal head and commander of the Titan Army was out to kill Percy since he was 12 and quite dedicatedly, and if that wasn't enough, he was wanted in multiple states for a false terrorism charge. And if you remember, he was rather ostracized at camp until after Titan's Curse.
Jason was the head of a legion, a praetor, revered by his comrades and already strongest among those he led or worked with. He had little exposure to any other extreme life death fatalities or any experience with being persecuted aside from the usual monsters and the legion training.
In conclusion, Percy beats Jason on land with a considerable margin; Percy beats Jason in the Underworld by an even bigger margin since Jason can't do much in the Underworld while Percy can control all the rivers of the Underworld and is used to the noxious environment present there. My apologies, but the near the sea comment made by op is practically delusional; Percy could literally sic any sea creature on Jason to take him out, doesn't even have to do it himself. Percy absolutely completely demolishes and disintegrates Jason near the sea.
Hot take. Jason is actually stronger and better at fighting than Percy. If they fought each other, Jason would win, even if they were at sea. Reading them fight together I'm now convinced. Percy making us believe otherwise is just him being an unreliable narrator