Ok I will start by saying I have been working so haven't been able to spend a lot of time during the day in each city.
Adelaide - very quiet and not as high rise a anywhere else. A very local feel to the place like everyone know everyone, a large aged population but still very good and varied CBD nightlife. Traffic around the CBD in rush hour terrible ! A bit cheaper than Perth for food and drink. Climate feels much more European.
Melbourne - a much bigger spread out city around the river which has plenty of tourist stuff.
Crown complex is awesome which is just part of a great nightlife. Cost wise not much different to Perth. Weather very variable though !
Sydney - the city is very London like in terms of how busy it is and have to say grimy compared to Perth but a very Asian feel and great selection of restaurants, shops etc at fairly reasonable prices. Lots of happy hours from 5pm to 7pm where you can get a pint for $3:50. Oh and at least you can get a train from the airport to the city !
In summary I like Melbourne a lot except the weather but Perth still wins for me as I've never been a big city lover.
Hope this helps, feel free to ask anything else !