If a man has a meat cleaver, he can not do as much damage as a man with a gun. Police have the responsibility to protect the people. If a man is threatening the safety of others with a gun and is surrounded by a lot of people, as in New York City, then police should absolutely do whatever is necessary to protect the innocent. A man with a meat cleaver is not as much of a threat as a man with a gun.
Normally I'm the first one to look for overreactions by law enforcement, but this incident SEEMS to be pretty clean. The suspect was waving around a meat cleaver and supposedly injured one of the officers present on the scene. The latest word that I have heard is that the suspect is going to live, so that's a lot better than the treatment most people get in situations like these.
It sounds as though Mr. Joudeh could pretty clearly be described as dangerous and disturbed. He was agitated, he was getting violent and he reportedly attacked officers with a meat cleaver and sliced one officer. That's a pretty dangerous situation, so I'm not surprised they shot him. I'm not sure what else they could have done.
No, police did not go too far because the man was armed and could have hurt a lot of people. Police need to take action when it saves far more people than it could hurt. There may be some backlash from the event, but police were there simply to protect.