There is a whole series of books about Percy Jackson, 'half boy and half god'. Unbeknown to us mere mortals, the randy old Greek gods are still coming down to earth to impregnate humans or get impregnated by humans. My daughter has just started reading these. The books are aimed at the same demographic that liked Harry Potter. The series may even be structured somewhat like Harry Potter. Poor Percy doesn't know his father is Poseidon, and seems quite normal except for his ability to sit at the bottom of the school pool for up to 7 minutes.
The movie had it's good points and the kids were pretty good. Again like Harry Potter, it features a trio of kids (2 boys and a girl) who get into and out of trouble because of their powers. I've seen all the Harry Potter movies, although I have not read, and have no intention of reading the books. My main problem with the first Harry Potter movie was that there wasn't enough story there. It was pretty much all exposition. And it helps to understand all of the Harry Potter movies if you've read the books. That's probably the case for most movies made from books however. In Percy Jackson, my main problem is that there isn't enough exposition. They could have cut down on some of the big set pieces (like the battle with the hydra) and spent a bit more time on why Percy was suspected of stealing Zeus' thunderbolt, and why Zeus left it laying around so some kid could steal it. These sorts of things don't bother my wife or daughter and they loved the movie. Your kids won't be bothered by those plot holes either so take them if they haven't already made you. You'll be entertained but don't think too much about the underlying logic.
There was some outcry against Harry Potter because of witchcraft and general paganism. I haven't heard anything along those lines about this movie. You can hardly get any more pagan than Greek gods.