The two became divided over the love of a woman, an empathic metamorph named Garuth. They both loved Garuth with such passion that the Kriosian empire fell. Krios eventually kidnapped Garuth from their homeworld and took her to the planet that became his namesake. This action started a war between the two worlds that lasted several centuries. (TNG: "The Perfect Mate")
For the planet sharing this name, please see Krios Prime.