I actually live in Sydney and I have lived in Melbourne. Melbourne has a far more efficient transport system where as Sydney's transport in in a state of near collapse. Sydney has far more crime and is way over-priced, Melbourne is better ran. However, both need to watch out as Brisbane might pinch the top spot as Australia's best city.
As for Canberra, it is allegedly "planned", a plan based on an assumption that oil would be cheap for ever (not now), it desperatly needs effective public transport. Canberra is also the country's only "true" inland city (other claimants are actually country towns).