As a Sydneysider...
Sydney V Melbourne... Syd is a city of landmarks. Melbourne is a city of culture and arts.
Most of what you want to see in Sydney can be done in a long good day. Two days if you want to stretch it out. If the Blue Mountains interest you, then add a day for that.
Seriously, I love my city, but if you have to make a choice, 2-3days really is plenty for Sydney.
Z...