The General also has the reflexes. During the fight between Kurono and the General in the alley even though Kurono was wearing the suit he realized that all his punches weren't connecting. He couldn't even touch him. Then the general knocked him fifteen feet away. The suit saved him. He got back up because he has determination and a strong will, but it was the suit that gave him the power to take the General down.
Izumi can hold his own against an opponent even without the suit. He proved this with the Shorty alien in the classroom and after his suit broke when he was fighting the vampire he was able to read his opponents movements and defeated him. The General took out several raptors on his first mission w/o a suit and showed his skill by beating up, what 30?, thugs on his own in tokyo.
The only fight we've seen between the General and Izumi was when Izumi went to Shinjuku. The General almost killed Izumi with his bare hands. If Izumi hadn't shot him the General would have definetly killed Izumi.