Having lived in Brisbane twice, Sydney twice and Melbourne twice over 25 years... they all have something to offer.
Sydney - great beaches and some stunning views. If you have enough money to live in the Northern Beaches it is a very compelling city. However, most people cannot afford that and are stuck 40k from the CBD in the Western suburbs. House prices astronomical even tens of kilometres from the good bits!
Brisbane - the winters are glorious, the summers can be stiflingly humid. Not as sophisticated as Sydney and Melbourne. If you like BBQ, swimming pools and not wearing shoes it's ideal. Housing still reasonably affordable.
Melbourne - easily my favourite city. Probably in the world, now that San Francisco has been trashed. The "Sporting, Music and Food" capital depending on who you ask. Very cosmopolitan, fantastic public transport, diverse and trendy. Very good food and coffee. The weather is much more like the UK...but with more sunshine in Summer. Housing can be extremely expensive and fewer and fewer bargain suburbs left.
It all comes down to personal preference.