They both mean the same, though omitting 'un' gives emphasis. For example 'Soy un hombre, entonces tengo bigotes' Is perfectly OK. My mother, who is quite old and a bit hairy on the lip, would probably resist any mention of this: "No tengo bigotes, ¡no soy hombre!" - 'un' would deprive this of its force. Similarly, 'soy un hombre de palabra' would be a bland statement of fact, 'soy hombre de palabra' would be an emphatic declaration, perhaps after an accusation of dishonesty.

Soy un hombre. = I am a man. Soy hombre. = I am male.