So far Kara had the most interesting roles in the show. She fucked up and set a plague on Metropolis then solved it with brute force, she tried brute force against Cheetah and failed, then Karen told her not to use brute force against the corrosive monster and she beat it, then she tried brute force against Livewire and failed, then she tried brute force against Giganta and failed, then tried brute force against Catwoman and failed but eventually used her wiles to solve her problem.
She almost gave her life to save Metropolis because Diana told her to kys herself.
I'm guessing Super Who comes directly before Fight at the Museum, either that or Kara's character arc wobbles a little.
All the other characters have a much more minor character arc: Babs learns to believe in herself in one of the shorts, Diana learns to stand up for herself in Sweet Justice, Karen learns to be more assertive in pretty much every episode about her and finally stays assertive in Super Who, Jess has zero character arc (so far), and Zee has a father-daughter episode coming up eventually which will probably be her only story arc.
So out of all the main characters, Kara has the most character.