I might be partial to Percy Jackson as a character because I found this second book the The Heroes of Olympus series to be much more exciting than the first book. The characters have better secrets to share, the threat is more immediate, and the quest for our lead characters feels more intense.
We pick up in time after the first book with the same evil threatening the world, Gaea, and the same prophecy of seven coming together. This time though, we're at the camp of the Roman demigods, Camp Jupiter, which we've never seen before, and Percy is our hero with a missing memory (you might want to check out the review of the first book so this makes a little more sense.) He wanders into camp, is questioningly accepted, and befriends two other campers, Hazel and Frank. Again, there are characters who know Percy's true identity, just like in book one, but they're keeping the truth to themselves to not disrupt the master plan (whatever that turns out to be.)
A quest gets issues to find and free Thanatos, who's basically the Grim Reaper, from a giant who also happens to be Gaea's son. They also need to help prevent an army of monsters from destroying Camp Jupiter. It's a tall order for three kids especially when they're all grappling with a very personal issue. In addition to Percy's memory loss, Frank is trying to figure out his family's big secret and how it applies to himself, and Hazel is wrestling with the guilt of a very bad deed nobody knows she's committed.
So all three set out to Alaska to fulfill their quest with nothing but the deeds they do to prove their character to each other and earn trust. They run into a lot of monsters, a few gods, and some other characters with mythological makings. Fewer immortals appear than in the Percy series and they mythology is very Roman-focused (which I know a lot less about,) so this book felt more like a pure adventure story to me than the first book of the series. I really enjoyed and it and am definitely Team Percy over Team Jason if such a thing exists.
Riordan continues to introduce compelling and intricate characters in extraordinary scenarios in his world of demigods that keep the pages turning. I think these are great YA books outside of the overly popular dystopian-framed books and are more worthy of your time to read if delving into this genre as a whole.