Huh. Interesting match up. I assume this is Alita in her final form/body?
Hawkman seems to hit harder with his mace and his axe can definitely do some damage, but without his weapon he doesn't seem to hit has hard as Alita.
More over, Alita looks to be the far better fighter and is faster, more agile and more acrobatic. Hawkman does have the advantage of flight though.
I'd say Alita takes majority, though Hakwman pulls a few victories via puncher's chance with his mace and flight.