I was going to say Monsters and Other Childish Things as soon as I read the title. It has a lot of support for the tone of How to Train Your Dragon (the films, at least - I haven't read the books). As you note, the kids aren't super powerful by themselves, but the monsters/dragons are. The relationships are very important and monsters/dragons tend to mess them up without realizing it.
It also makes it pretty easy to customize your monster/dragon to do what you want. And it's a really fun game in its own right.