Being a Philadelphian who now lives in Sydney, I can answer the question about comparing the term "suburb" in the two places.
Technically, the city of Sydney is quite small, as is the city of London. All of the pieces surrounding the official Sydney, but that constitute the actual inter-city are called "suburbs" (as they are in England). So suburbs can be quite urban. They can also be iner-city slums.
Most American cities (perhaps Boston is an exception) seemed to incorporate the outlying areas as they became a de-facto part of the city. Once they are incorporated they are no longer called "suburbs".
As a matter of fact Woolloomooloo is an urban area. It is considered inter-city (but far from a slum). From old photographs I have seen, it looks like it was a poor-but-honest area up to the 40s or so.