They are pretty much the same. 'iż' seems to be more old-fashion or formal version of 'że' and it isn't used much these days (unless in literary works). When speaking, a Polish person isn't going to use 'iż' at all; they will always use 'że' instead.
"Iż" actually is being used a lot in modern polish. Since we shouldn't repeat words in one sentence we use both of them to make text look neat.
Example:
Mama powiedziała, iż Tato juz wie, że obiadu nie będzie.
