In the most basic of senses, the explanation for the differences between Bruno and Gretel is that one is an example of how people conformed to Nazi thought and how people rebelled against it. While Bruno and Gretel are raised in the same house with the same guidance presumably from both parents, their fundamental choices about how to view the rise of the Nazi culture that is around them represents their differences in characterization. Gretel recognizes that a certain amount of power comes from capitulating to the Nazi social setting. She recognizes that "popularity" comes from being a part of this "clique." It is for this reason that she fully embraces the trappings of Nazism. This includes the worship of Hitler, the pictures of Nazi leadership, the flirting with Kotler, as well as the belief that her own prestige can result from being an accepted part of the Nazi social elements.
On the other side of this would be Bruno, who repels the Nazi constructed view of reality. He does this innocently enough, in terms of asking questions about "the other" in reference to who these people are, why they look the way they look, as well as his dislike of "Out- With" and "The Fury." Bruno also seeks to develop his own path to contentment, one that lies outside of what the established social path of the Nazis entails. An example of this would be the tire swing and the questioning of Pavel's identity. Another example would be the wandering to the end of the fence and his friendship with Shmuel. As the narrative develops, Bruno takes active steps against what the Nazis represent in terms of fulfilling his friendship to Shmuel. In the end, his commitment to his friend is not only what causes his death, but becomes the ultimate statement against Nazism. It is here where the differences between Gretel and Bruno are the most pronounced, as it shows how the paths taken in how one views an unjust society can result in massive differences between individuals. Gretel and Bruno demonstrate this.