Disclaimer: As the Idea Guru, my knowledge is mostly theoretical. War is not theoretical.
There is a lot of variance in an elements ranking from war to war. This indicates to me that either player skill (including all skills involved in War) or luck has a higher impact on the results than the element chosen. However if we look at the extremes of Fire and Water (sorry man) we can see that either Water gets abnormally bad skill/luck (extremely unlikely) or the element chosen does still have a visible impact.