Warning! Spoilers for Supergirl: Woman of Tomorrow #2 ahead!
Batman. Supergirl has many qualities that make her a great hero and she has proved many times that she's as good as Superman. She is often seen as "twice as good and second best" to her cousin. This is due to him having arrived on Earth, and in the comics, before her. Therefore, she has always been overshadowed. Now, in Supergirl: Woman of Tomorrow, Supergirl's journey across space promises to see Kara Zor-El finding meaning in herself, away from Superman.
Batman is a hero with a dark side. He is notoriously moody and can be quite brutal when it comes to his methods. Despite Batman's ever-growing darkness, he always maintains his number one rule of not killing. The same goes for Supergirl, who, in issue one, explicitly denies Ruthye's plea for her to kill her father's killer, Krem. However, it seems Supergirl's mind has changed about her strict rules. This happens after Krem shoots and kills Krypto the Superdog, Supergirl's best friend. Now, Supergirl makes her way on a space bus to hunt Krem with Ruthye.
In Supergirl: Woman of Tomorrow #2 by Tom King and Bilquis Evely, Ruthye asks Kara if she ever thought of pursuing revenge for her family's deaths. Supergirl doesn't hesitate to answer as she gives a resounding "no." This shocks Ruthye as the first thing she thought of when seeing her father's dead body was revenge. Supergirl being the person that she is, would never think of such an idea. And while she wanted to get back at Krem for killing Krypto, she also reveals in this issue that she can't even what Krem looks like.
This is a staggering revelation that suggests that Supergirl's obsession isn't as strong as readers thought. Normally, it's been said that facing off against a killer, people never forget their face. But Supergirl didn't even him and now has no recollection of his appearance. Obviously, Supergirl's anger during Krem's attack was a temporary thing. But it's enough to make her pursue after him, despite not being obsessed on a level anywhere near to Batman's endless fixation on his parents' murderer.
Batman's pathological obsession with Joe Chill is the complete contrast. He can recall Chill's face, despite being a child at the time of his parent's killing. Batman's obsessive need to protect Gotham stems from his initial fixation on Chill. And from then onwards, Batman became obsessed with fighting all crime and won't rest until every criminal is put down. Supergirl is nothing like Batman, despite suffering a tragedy that could have made her like him. And the fact that she can't Krypto's killer's face runs this point home. Supergirl: Woman of Tomorrow #2 is available now in comic book stores and on digital platforms.