The expression “six of one and half a dozen of the other” means: No choice; one and the same; even steven.
There seems to have been no specific allusion involved in this expression, nothing beyond the fact that half a dozen is six.
It first appeared in Marryat’s The Pirate and the Three Cutters (1836).
Several of the sailors, repairing the ravages of a storm, have fallen to talking about some of the passengers, especially about the black nurse of white twins on board.
Jack says to Bill, “You’ve been sweet on that girl for these last three weeks.”
“Any port in a storm,” Bill replies, “but she won’t do for harbor duty, it’s the babies I likes.”
At which Jack jeers, “I knows the women, but I never knows the children. It’s just six of one and half-a-dozen of the other, ain’t it, Bill?”