We are in Sydney and really like it. Everyone talks about how expensive it is here, but I think it is perfectly affordable for a small family. I will give you an overview of our finances. Our combined income is 150,000 dollars pa. After tax we get just shy of 9,500 dollars a month (go to www.paycalculator.com.au/ to see how much money you will get a month).
Out of that comes rent: 3,500, daycare: 2000, food: 600, petrol and tolls: 300. Which leaves about 3000 dollars a month disposable income. We have a modest lifestyle, so put about 2000 dollars away in savings. Note that we should get the Childcare Rebate (one day!), so daycare should go down to 1,500, if I have calculated correctly.
We are me, DH and DD who is 3. We are living in a 3-bed house (too big for us, so are thinking of getting a lodger to help with the rent) in Sydney's inner west. It is a gorgeous area and we love it. It is as historic as Sydney gets, with water around us, lots of parks, a buzzy street life and a view of the CBD.
We have far more money than we had with exactly same jobs as in UK. The idea of saving in the UK was laughable, but now we can put away nearly a thousand pounds every month, even living the most expensive city, in one of the most expensive suburbs in a house with a garden that is too big for us! Happy days! www.domain.com.au will give you an idea of the cost of housing.
Of course there are flies in the ointment. The traffic is mad and I can spend hours in the car each day. It can be very difficult to a place in daycare (I wish that I had known that DD could go to the local public school's kindergarten, which would have saved money and start her off with her new schoolmates). The lifestyle can be very aspirational, in my local shopping arcade (for groceries!) there is a laser and filler salon. Nail bars and morning lattes seem to be the norm. But on the whole, we can afford to live here with no problems.
I have not been to Melbourne, so I can't say how they compare, but imho it is the coastline that makes Sydney so special. The number and variety of beaches, the walks along the shore, the seaside communities. But there is little to do when it rains or in the winter that doesn't cost a fair bit (or not that I have found). Good luck with whatever you decide.