Brief applies especially to duration of time (a brief stay in a hospital). Brief also means "concise," "curt," and "succinct": "The chairman made a brief talk of only five minutes." Short applies to both time and space: "That was a short meeting." "Joe is a short man." It is informal to refer to "a brief distance" or "a brief skirt." That is, short can be used in almost any situation, but brief should be applied only in circumstances involving time.
Dictionary of problem words and expressions. Harry Shaw. 1975.