All the best with your move. It sounds like Melbourne is defo more the place for you at this point in your lives. You tried Adelaide, gave it time and are confident in your decision.
I never stack Adelaide alongside the major cities in the UK because it really isn't like a major city along the lines of a UK one. I view it on par with the likes of our smaller cities and that works for me. I personally don't want to live in any city in the UK and am happy to move back to Adelaide over any of the other large cities in Australia. We currently live about 9 miles from Bristol and while its good for shopping, eating out and cinema etc on occasion we certainly have no interest in clubbing and bars and so on.
If someone said to me to live in Manchester, London or Birmingham here I'd refuse. I'd loathe living in a city like that as it has nothing I want or need on a permanent basis. Not one thing appeals about those sorts of cities, so I choose not to live in one ;) But millions of people do like that kind of city living, living in large cities. Makes for a good mix and allows each of us to find the right place to call home :)