On the aspect of getting opportunities, which is best? Sydney or Melbourne?

Answer 1

My impression is that Melbourne runs on "old boy" style networks more than Sydney, although that is breaking down.

Sydney is new money, faster and more adventurous than Melbourne. I don't think that there is any doubt that in the last 20+ years the financial balance in Australia has shifted decisively to Sydney. Sydney is where the economic power is. Melbourne is old money trying to work out "How did that happen?"