Grew up in Sydney, early adulthood in Brisbane and around SE and central Queensland, 30's spent in Melbourne.
Melbourne wins hands down as the best city for my money. Queensland is cool if you're into outdoorsy stuff. The weather is almost always good, winter lasts for 4 weeks and still hits low 20's in the middle of the day. It can be very parochial and redneck though, and it's pretty conservative. Lots of good places to go, nature wise - everywhere else is cookie cutter chain stores that are exactly the same no matter which part of the city you're in. It's the cheapest of the three places to live.
Sydney I left when I was 12 but was usually there 3 times a year. It's much more money focussed, much more rushed in terms of pace, and very expensive. People are ok once they know - it's convincing them you're worth getting to know that's the hard part. Stunning natural spots very close to suburbia and that spectacular harbour. There are some very funky corners in Sydney. Overall, it's more a pub city than a cafe city. It shows it's age a lot more than Brisbane or Melbourne I think.
Weather in Brissie and Sydney is usually more toward the humid side of things in summer. They both have spiders, cockroaches, mosquitoes, flies and the occasional snake in the garden. Both have great access to very very good beaches. If you want beach culture, you want Sydney (or Brissie, but you'll have to travel further).
Melbourne lacks any standout 'wow' areas - there's not much you can take visitors to and say "Check out how fucking cool my city is!" - but once you've lived there for awhile you won't want to go anywhere else. People are friendly, not nearly as conservative as in Brisbane, more laid back than in Sydney, I never had trouble creating work for myself and earned very good money when I lived there. Great food, lots of cultural things to do if you're into the arts. In summer - usually February, you'll get a week or two of blistering hot weather where your furniture will melt and your elderly neighbour will most likely fall over dead. The rest of the year is very changeable. Winter is worse than Sydney or Brisbane. Melbourne gets a lot of flack for having four seasons in one day, but it's true. It's often wet, but also often windy or sunny an hour apart. Outdoorsy stuff is also readily available but you're more likely to be reading the weather forecast than you would in Brisbane before you go. Beautiful areas though and much more accessible than in Queensland because the state is so small. Rent is a shitstorm at the moment if you plan to move close to the city (but I think that's the case in Sydney too). And you have the Australian Open tennis, the Melbourne F1 Grand Prix, the Melbourne Cup horse race and Tony Doherty's gym in Melbourne!
And no huge hairy spiders, mosquitos or creepy crawlies. You get the odd rat and if you swim at the beaches in Melbourne you may well get taken by a shark, but they're small prices to pay!
I'm living in the edge of the Black Forest in Germany now, which is also very pretty, but there's not a day that goes by when I don't think about moving back to Melbourne. Can't say the same about anywhere else in Oz.
