'Drunk' can be used as a noun or an adjective. For example, "He was a drunk." (used as a noun), or "He was too drunk to drive." (used as an adjective). 'Drunken' on the other hand, is only an adjective. For example, "He was a drunken mess." You can't call someone "a drunken", so that's where they differ grammatically, I think. In your example, "a drunk/drunken man", both the 'drunk' and 'drunken' are used as adjectives, so there's no real difference beyond preference, but using 'drunken' is probably a bit stronger as an adjective than 'drunk'. Also, I think people more commonly prefer to use 'drunk' as an adjective instead of 'drunken'. Another noun you could have instead of calling someone 'a drunk', is 'a drunkard', but that seems a bit stronger as well.

I'll try my hand at this question. Drunk can be used on its own to describe a person, in the sense of here and now. So you can say: He is drunk. Meaning he is currently intoxicated with alcohol, but he may or may not be a person who habitually gets drunk. Drunken is descriptive of a continuing condition, like: He is a drunken. Meaning that he habitually gets drunk or that he is an alcoholic or borderline alcoholic.