Reading up on the types of love has helped me understand what I like and dislike about the different Disney princesses.
When you think about how a Disney princess exemplifies love, the relationships for many of the early princesses—Cinderella, Snow White, and Aurora—appear to be focused on eros, at least as far as the princes are concerned. Mulan’s interest in Shang starts with eros, but her feelings evolve into respect and admiration for his character, not just his eight-pack. Even Ariel only demonstrates eros for Eric, whom she does not know at all except by sight.
As much as I adore The Little Mermaid, her relationship with Eric is extremely superficial and borders on mania. I mean, she gave up her voice for a man. Rapunzel also shows mania, given her determination to see the floating lanterns.
As far as ludus, Belle, Jasmine, Rapunzel, Anna, and Tiana show the building of their relationships through romance. To a much lesser degree, Mulan and Shang flirt, but they snip at each other more than anything else.
Of the princesses demonstrating philia, the most obvious is Mulan, who saves first her entire troop on the mountain and then the emperor through the end of the movie. Anna demonstrates this in Frozen 2 when she awakens the mountain trolls.
By the time Frozen 2 rolls around, Anna and Kristoff have reached as close to pragma as any Disney princess can through the short duration of the films. The best example I can offer is Mulan’s parents (who actually survive the story!) and the sorrow they share when her father is preparing to leave. Rapunzel’s parents also appear to share pragma in their grief and hope for finding their missing daughter.
While Snow White, Aurora, and Ariel appears to share storge for the fairies, dwarves, and King Triton respectively, Cinderella doesn’t really have a loving relationship with anyone except her animal friends. Rapunzel even shows storge for Mother Gothel, despite the abusive control she exhibits to her adopted daughter. Mulan goes to war out of storge, because she doesn’t want her father to die. Similarly, Belle sacrifices herself as a prisoner to the Beast for her father. There is also obvious love between the sultan and Jasmine, as well as between Tiana and her family. The storge of Anna for Elsa forms the crux of both Frozen plots, and Elsa eventually shows the same deep-rooted affection for her sister by the end of the first movie. More heartbreaking is the storge Moana has for her family, especially her grandmother.
Philautia is a little harder to observe, but Belle refuses Gaston because she knows she deserves better. Jasmine also appears to express her self-worth as she tells Aladdin and Jafar off for imagining they know her life better. Tiana knows her worth, too. She has a plan to run her own business, and she knows she has the skills needed to succeed. The rest of the princesses seem to significantly lack any sense of self-worth. In the case of Mulan, this is unfortunate, since the historical character went on to become a decorated commander. She would not have been so successful had she lacked faith in herself, which Disney reinforced through the song “Reflection” as well as her botched matchmaker visit.
Finally, we come to agape. The first example that comes to mind is Moana, who is willing to sacrifice everything to save her people and is even able to find empathy for Te Ka, who is actively trying to kill her. Anna also exemplifies agape. She runs off to find her sister in Frozen to save all the people of her land from the endless winter Elsa has unleashed. The lesson of agape comes to Elsa a little later, but she goes into the unknown past to save a bunch of strangers who have been trapped by weird magic, and then, after her sister breaks the dam, races to rescue Arendelle from the coming wave that would have destroyed the homes of all her people.
Largely because of the way they demonstrate different forms of love, Anna, Elsa, Moana, and Mulan present as more heroic and far less hollow than their fellow princesses.
Obviously I don’t own any of these Disney characters. They make a good resource for study because of everyone’s familiarity with their stories. I also chose to leave Pocahontas out of this analysis to avoid conflating the Disney character with the historic one.