Knowing and recognizing only himself
Throughout Final Fantasy IX, Zidane shows up for as many people as he can with profound kindness in his heart. He possesses the emotional intelligence to recognize when others are in pain and if they should have company or be left to their devices. This compassion is what propels him to dive into the rampaging Iifa Tree in order to rescue Kuja at the end, knowing that their roles could easily have been reversed. In doing so, he makes it so that Kuja doesn't die alone.
For much of the story, Kuja is nothing like Zidane. He's selfish and cares only about himself, viewing Gaians and black mages as lesser beings to be used for his gains. He has a sadistic streak (and a torture chamber in his abode to indulge the need!) that relishes exerting his influence on those weaker than him—a compensatory mechanism meant to offload the crippling weight of his own imprisonment as Garland's slave.
Kuja: The weak lose their freedom to the strong. Such is the way of the strong. And it is the providence of nature that only the strong survive. That is why I needed strength.
Kuja is undeniably intelligent and well-read, storing many a book in the Desert Palace. Even so, it's a wonder how he, with his limited emotional quotient, was able to manipulate the once kind-hearted Brahne into slaying thousands and destroying entire countries out of greed. It could've been a learned tactic from the many plays he's watched and read. It could also be that he saw something in Brahne that he knew he could exploit, because he could recognize it—the fear of death.
A glimpse into Brahne's history in the Ultimania's timeline reveals that she'd lost many of her loved ones at a young age until there was nobody left, save for her surrogate daughter. As a ruler, she'd been warm and kind, yet undoubtedly griefstricken as a person. It's possible that Kuja transposed his desire for control onto Brahne, who'd lost so much and would have been enticed by such honeyed words. By seizing whatever lay within reach with the unstoppable might of the eidolons, she would have possessed everything, all while ironically forgetting why she desired such a thing in the first place by jeopardizing the life of her daughter.
Tangentially, Brahne and Garnet together serve as narrative parallels to Kuja and Zidane. Garnet illustrates her undying devotion to her beloved mother while Zidane demonstrates his compassion when he forgoes his dislike of Kuja to dive after him in the Iifa Tree. This parallel is also why both Brahne and Kuja find clarity in their dying moments, for death is the ultimate equalizer. When all possessions falls to the wayside before death's door, there are only the people who remain. By having Garnet and Zidane at their sides, Brahne and Kuja find their respective peace before passing.
Kuja not only bears narrative similarities to Brahne, but he also must have recognized some of her qualities. Like the black mages who put to mind his unwanted fate as a Genome, he could have related contemptuously to Brahne, and therein lies the possible third reason on the topic of why he treated her so poorly compared to Hilda. Whereas Brahne and the black mages reminded him of tasteless inferiority, Hilda's predicament as the spurned wife who'd been momentarily "replaced" by a mistress could have triggered a more bittersweet kind of familiarity. He might even have relished her vengeful spite if he knew that she'd bitten her thumb at her adulterous husband by turning him into an oglop.
It's because Kuja is so self-obsessed within the confines of FINAL FANTASY IX that he can be called empathetic. His ability to understand behavior outside of himself is poor, but he knows himself, and so he reacts more strongly—for better or for worse—to those who mirror him in his eyes.