Suggested by Sonic Harley Quinn is definitely a character who has been getting a lot of screen time recently. She’s an excellent hand to hand fighter and even got superhuman abilities for a while. That said, Hawkgirl easily wins this round. She became a Black Lantern at one point which gave her a whole slew of great abilities and additionally she already had super strength and some slight healing regeneration. In a straight fight I don’t see any way Harley Quinn can even try to turn the tides of battle. Hawkgirl wins.
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There’s a reason Hawkman/woman doesn’t visit Gotham. It would hardly be a fair fight for either. Just Hawkgirl, however she got her powers, could defeat Harley Quinn blindfolded.
Yeah Harley Quinn just isn’t ready to deal with someone like Hawkgirl. Hawkgirl’s hand to hand is better I’d say and her physical abilities are also more impressive.