At each kingdom, a contest is held to see which princess is the best in which category. Series-wise, these parties appear to be held only as a show-off of the talents of princesses when pitted together in an intense competition. Princess Parties are often to boost the reputation of kingdoms, but other than that, it is a way for princesses to socialize, have fun, and be creative with challenges.
At the Princess Party, each of the princesses were supposed to dance with Prince Bright, and whoever had the best smile won. After encouragement and help from Fine and Rein, Lione won the contest and was deemed the Best Smile Princess of the Wonder Planet.
BestdecorPrincess
Kingdom: Meramera (Flame) Kingdom; Sunny Kingdom (manga) Episode: Episode 5; chapter 11 (manga) Winners: Seed Princesses; Fine and Rein (manga)
The Seed Princesses weren't satisfied with their jewels, so Fine and Rein helped them with their Decor Maker. Eventually, their jewels outmatched even that of Altessa's, since they put their own hearts and friendship into making their own decorations.
In the manga, Fine and Rein made jewels for each other with the Decor Maker as an apology for fighting. When they wore these jewels to the Princess Party, they ended up winning.
Altessa had a high chance in winning because she was talented at making pastries, but when Fine and Rein use the Prominence to get the ingredient Lione needed, the vibrations of the sumo wrestlers destroyed Altessa's cookie castle. Since Lione was featured with trying to make pastries from her own heart, it was probable that she'd be crowned, but she ended up not winning the party. Milky was chosen, because her food was the next favorable. (It's kind of obvious that Milky'd be the runner up because of her major love for sweets. ♥)
In the manga, Milky still won, despite the different scenario that took place.
Originally, it seemed like Sophie was going to win, because she was good at shooting balls into a basket; however, when it came to the ball-throwing, Altessa and Sophie started throwing balls at each other, wrecking the portion of the contest. After Rein used the Hane no Mewgram on them, Milro encouraged the girls to do their best. Because she showed the most sportsmanship, Milro won, even though before she thought it was hopeless, since she doesn't seem to be athletic.
In the manga, well, the not-so-athletic-as-the-anime-portrayed Lione finished the race first and won. It was all because Rein told her she could do it. ♥
BestflowerPrincess
Kingdom: Moon Kingdom Episode: Episode 25 Winner: Sophie
Altessa looked like she was going to win, since she has a major talent in flower arrangement, but Rau and Yan locked her up in a carriage before she could even attend the party. When Fine and Rein find her, they accidentally set flower-devouring locusts loose into the palace (the original plan of Rau and Yan). Sophie, concerned about Altessa's absence, took her spot to stall time when it was Altessa's turn to present her flowers, and when the locusts struck, she stood in front of Altessa's roses, refusing to let the locusts touch them. She was crowned the Best Flower Princess because she had shown compassion to protect one's work when her own was destroyed by the locusts.
BestArtsPrincess
Kingdom: Water Drop Kingdom Episode: Episode 36 Winner: Altessa, who later refuses the prize
Milro had the best chance of winning, since the attendees of the party absolutely loved her work. When Bright showed up, he cast a spell over Yarmul and Pump, forcing them to make Altessa the Best Princess. After Fine and Rein defeated Bright, Yarmul and Pump were still going to make Altessa the Best Princess but Altessa refuses. She believes that the title should be earned by hard work and declares that she'll give it her all in order to become the Best Princess.
This was a major surprise, considering Fine and Rein haven't won Best Princess yet, but when the party commenced, it was obvious that Altessa would win, especially with her dance with Auler. When Bright appeared again, he tried to make Fine the Best Princess, but Fine gives the title to Altessa. As Auler presents Altessa the medal, Altessa gives Auler the medal for being so kind to her.
BestDressPrincess
Kingdom: Sunny Kingdom Episode: Chapter 3 (manga) Winner: Lione, Altessa, Milky, Sophie, and the Seed Princesses
A manga-only Princess Party, Milro had the upper hand considering her dress glittered prominently under the lights. Fine and Rein used the Prominence to make the other princesses' dreses glow and the rest of the princesses defeated Milro.