With any new children’s fantasy, comparisons to Harry Potter are inevitable. J.K. Rowling sets the standard for books that connect with kids (and adults, too, for that matter).
As far as similarities between Percy and Harry, I would say a couple of things:
First, recognize that Percy Jackson and Harry Potter are similar because they draw on the same sources in folklore and mythology. The idea of a young boy finding out he is special, training to use his abilities, and defeating an evil villain to take his rightful place in the world -- this is the story of both Harry and Percy. It's also the story of Perseus, Theseus and Hercules -- narratives that are over three thousand years old. Most of the elements people point out as similarities between the two series come straight from mythology. The Harry Potter series uses folklore and mythology to beautiful effect, but J.K. Rowling did not invent these elements.
Secondly, Percy and Harry are very different kids, who live in very different worlds. Camp Half-Blood is full of magic and mystery, yes, but it has a unique flavor that is totally unlike Hogwart’s. Percy and Harry come from different backgrounds. They don’t have the same issues with parents. Percy’s a bit more of a troublemaker than Harry, I think. He’s used to being labeled the “bad boy” and has gotten kicked out of numerous schools (though this is never entirely his fault). Harry is likely to restrain his friends if they get in a fight. Percy is more likely to punch a bully in the nose. They do share common ground — both have enormous power and responsibility thrust upon them before they are ready. Both are brave. Both have to face their worst fears and rely on a small group of loyal friends. But their stories are quite different. I think readers will see that when they read The Lightning Thief.
Having said that, do I hope readers of Harry Potter will enjoy my series? Of course. Any comparison to Rowling is high praise, because I’m a huge fan of her work. I totally understand why kids love Harry Potter. The effect those books have had on young readers is hard to overestimate. In my years as a teacher, I’ve never seen anything that energizes students like Harry Potter. I used to come into my classroom and find students reading Sorcerer’s Stone for the thirteenth or fourteenth time, just because they wanted to. I would say, “That’s a great book, but aren’t you getting tired of it?” The student would always look at me sadly and say, “Yes, but there just isn’t anything else this good.” After hearing that for a few years, I realized there was an unfulfilled need for more children’s literature that impacted kids the way Harry Potter did. I decided to try doing something about it — I knew young readers. I understood what they liked. The Lightning Thief is the result. Whether I succeeded or not, I’ll let the kids decide.