Does city influence what suburb is like?

Can you tell anything about a suburb by knowing the size (and other factors) of the city to which it is a part? In other words, are two suburbs, each with a population of, say, 20,000, and are located in a section of suburbia developed at the same time and are made of up subdivisons and sprawl, in the same region,but one is a suburb of a city of 2,000,000 and the other a suburb of a city of 750,000 very much alike or do they differ in nature because of the size (and importance?) of the city to which each is attached?>