I prefer "eggs is eggs", even though it's ungrammatical, as it introduces a down-to-earth and slightly humorous tone into what may be an earnest conversation or piece of writing. It seems it first appeared in print in Tom Brown's Schooldays (1857).
I'm not convinced by the "x is x" origin. Eggs are used in a number of stock phrases and proverbs so it would be natural to coin another one. The use of "is" is dialectal so I think the phrase was begun by people of little or no education, certainly not people who rubbed shoulders with logicians.