Princess Anise for Queen!
Seriously, her brother's priorities are all wrong. Instead of trying to be better or comparable to his sister in terms of flashy feats, he ought to be focusing on why it is his sister is so admired and renowned. Is it her feats per se? Or is it her innovative, creative spirit? The Prince's main issue doesn't seem to be that he's inept, but rather that his vision of the world is too narrow. If he knows that Anise's rep comes from innovation in magicology, then he could carve his own rep by looking into things she isn't, like agricultural reform, political reform, military reform, economic reform, etc. Anise herself is so focused on the research parts that he could very easily have forged a partnership with her and become known as the future king who spread modern magical tools for the benefit of all. Instead, he wallows in his insecurity.