Both are correct You can see a man do an action; here you just state what he does/did or You can see a man as he is/was doing the action. This way of speaking is more descriptive
I think the two sentences have a different meaning. Maybe they are both correct...
Certain verbs of perception are followed by either the simple form of a verb or the -ing form of a verb (The -ing form refers to the present participle). There is often little difference in meaning between the two forms, except that the -ing form usually gives the idea of