No, the main characters in Harry Potter pretty deliberately do not seek power - actually a key plot point in the final book was Harry choosing not to try to acquire powerful items that might enable him to overpower his opponent, but rather to do as his mentor had suggested and pursue Voldemort’s weakness. A key difference...
Harry never seeks to become more powerful. He does learn new spells, but what he is learning is to apply the power he already has. To use what he’s been given. That’s an idea that should resonate with Christians...
Comparing the magical systems in Harry Potter to those in LotR is silly, they’re not parallel at all. People who criticize Potter’s magic obviously don’t write themselves. They don’t understand that when writing a story, you’re inventing a whole different world. Sometimes it looks a lot like ours, but the rules are different. In Harry Potter, the “rule” is that magic works and is not forbidden. In our world, magic neither works nor is licit. But Potter does not take place in our world. If I wrote a science fiction novel in which entropy did not exist, would I be trying to tell children that they can ignore entropy like my heroes? Of course not.
But one of my early criticisms of the series, and a topic that doesn't ever get discussed on HPITD threads, is a recurring theme that 'HP can get away with bloody murder; break any rule and face no consequences because he's ~special~'. JKR did a good job of exploring the impact of that on HP's relationships with friends and family as the series progressed. It was the source of a lot of conflict, and towards the end, self-searching and growth - which I applaud. However, I was really bothered at the beginning with her gratuitous treatment of the ultimate child fantasy: "I'm so special that I can do whatever I want and no one can tell me what to do." Those kinds of notions do far more to undermine parental authority than make-believe magic ever could.