The two alternatives are the same, as in Either Route 2 or Long Avenue will get you there—it's six of one, half a dozen of the other. This term simply equates two different ways of saying “six.” [First half of 1800s]

The alternatives are the same: “I can take the bus or the subway to get home; during rush hour, it's six of one, half a dozen of the other.” The phrase, which is sometimes inverted as “half a dozen of one, six of the other,” is merely two ways of expressing the number six.