Divas are almost always likely to slap Sims when being insulted, unless they also have the good trait.
Divas will take a -30 relationship hit when having an argument with their romantic partner. There's also a 65% chance they will break up after an argument.
Divas are difficult to be friends with; their relationship meter raises more slowly than other Sims, unless they or the Sim talking to them has a trait that allows you to become friends more easily, such as friendly.
Divas will get the "Well, Duh!" moodlet whenever they receive a compliment, instead of the "Flattered" moodlet.
Mirrors add extra environmental score for divas in a room.
Other Sims may accuse others as a diva, which is a mean interaction. However, if the person accused is a diva, they get a positive relationship instead. Accusing other Sims as a diva enables Sims to learn that the other Sim has diva trait. The animation used when accusing a nondiva Sim is the Sim pointing to another Sim, with a speech bubble that contains the accused Sim's portrait.