Spider-Man more often than not - and mostly because of his webbing, not his agility. If she gets in close the matchup evens out, her strength/damage soak/healing factor/nth metal senses against his reflexes/speed/agility/spideysense.
http://s125.photobucket.com/user/DCHawks_photo/media/BB044-11.jpg.html
It should be noted in this scan posted earlier Hawkgirl and Hawkman are dodging invisible bullets from an invisible sniper rifle (or at the very least scoped rifle. idk anything about guns).
http://s125.photobucket.com/user/DCHawks_photo/media/hm-37-02.jpg.html
... and in that scan she throws what looks like a revamped kusarigama hard enough to penetrate a steel car door with the blunt end, hook into it, and casually rip it out without leverage.
