Thanagar is right in the middle of the humanoid aliens of Krypton and the more alien-aliens you see in GLC like Salakk, Tomare and Kilowog.
Their differences are mostly subtle. The most obvious quality is their wings which are sometimes, other times artificial. They are also more stronger and more durable than ordinary humans, have enhanced senses and can naturally communicate with birds (which implies that part of their minds are wired like birds).
Thanagar also has more alien like creatures like the reptilian based aliens and more hawk like aliens as well.
Pre-Hawkworld Katar and Shayera weren't harsh. They were probably the most benign and softest members of the League to the point where it upset them when they had to fight their friends in Shadow War of Hawkman.
I should note that one of 'bad aids' for trying to fix the Hawkworld mess Post COIE was claiming that the Hawkman on JL was actually the reincarnation Hawkman (and later on it was Fel Andr as a sleeper agent). That guy definitely had some rough edges especially after Johns brought him back and his aggressive side was in full display around 'Crisis of Conscious', the Black Adam arc in JSA and a period in his own ongoing after being captured and tortured by some villains.
Katar and Shayera are also scientists at heart and not just cops and their scientific expertise and gadgets (which they built themselves) played a bigger role in JLA stories than their archaeology and cops sides.
On JLU, Shayera was the berserker and while I like the 'tough girl' personality of the character, I can't help but think that much like John Stewart, the over emphasis on the militaristic aspect of her character has lead to the decline of the more thoughtful and intellectual aspects of their characters.