First off OP said Hawkman has the Claw, not sure how Aquaman will win
Also....
Originally posted by -K-M-
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Battles
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Shadow War of Hawkman #3: Aquaman (Hawkwoman)
Here with one of their guns Hawkwoman quickly knocks out Aquaman
1. http://s125.photobucket.com/user/DCHawks_photo/media/ShadowWarofHawkman03-19.jpg.html
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Hawkman #15 : Aquaman (Hawkman: Holl)
Hawkman tracks down the avatar of the Baracuda, but must go through Aquaman who was friends with him until he found out he was a child molestor. Hawkman schools Aquaman
1. http://i125.photobucket.com/albums/p68/DCHawks_photo/Hawkman-v3-015-13.jpg
2. http://i125.photobucket.com/albums/p68/DCHawks_photo/Hawkman-v3-015-14.jpg
3. http://i125.photobucket.com/albums/p68/DCHawks_photo/Hawkman-v3-015-15.jpg
4. http://i125.photobucket.com/albums/p68/DCHawks_photo/Hawkman-v3-015-16.jpg
5. http://i125.photobucket.com/albums/p68/DCHawks_photo/Hawkman-v3-015-17.jpg
6. http://i125.photobucket.com/albums/p68/DCHawks_photo/Hawkman-v3-015-18.jpg
7. http://i125.photobucket.com/albums/p68/DCHawks_photo/Hawkman-v3-015-19.jpg
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JLA #119 : Carter Hall
Here Carter subdues a mind-controlled Aquaman
1. http://i125.photobucket.com/albums/p68/DCHawks_photo/JLA119-0006.jpg
In all seriousness without the Claw Aquaman should win against pre 52 Hawkman. I know nothing about current Hawkman though