Oftentimes, "zij" is used to provide emphasis:
- Waar is Mieke? Ze doet de afwas. -- Where is Mieke? She is doing the dishes.
- Wie doet de afwas? Zij doet de afwas. -- Who is doing the dishes? She is doing the dishes.
They are generally interchangeable, however. When not emphasising, "zij" can provide a more formal feel than when using "ze". Most people would use the latter in this scenario, at least where I live.