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.
Mama powiedziała, iż Tato juz wie, że obiadu nie będzie.