In the Hakumen's arcade mode, both of them fought to a stalemate and Azrael had to walk off while Hakumen says "Even you know when to back off."
As for Bullet vs. Makoto, I disagree that Bullet would beat Makoto. Makoto is able to manhandle Tager in her CS arcade and beaten the living hell out of Izayoi in CP arcade. Izayoi is one of the strongest characters ever and Bullet is unable to take on a muscle-bound prick like Azrael. Plus, Makoto held her own against Relius Clover back in her CS story mode.
Kagura's men couldn't keep up in capturing Makoto while she was trying to locate Tsubaki. A lot of characters compliment her physical prowess many times in story mode.