The main difference between the two Eggs is that the East Egg contains mostly families with hereditary wealth; "Old Money," passed down through generations. Their belief is that breeding and station comes from within, with their families set up as symbolic nobility for the rest of the city. The West Egg, in contrast, contains many families of "New Money," who have earned or otherwise come into their wealth recently, perhaps in a single generation. The East Egg looks down on the West Egg, considering them to be pretenders who aspire to a social status to which they are not entitled. Even Daisy is somewhat disgusted by West Egg:

She was appalled by West Egg, this unprecedented "place" that Broadway had begotten upon a Long Island fishing village -- appalled by its raw vigor that chafed under the old euphemisms and by the too obtrusive fate that herded its inhabitants along a short-cut from nothing to nothing. She saw something awful in the very simplicity she failed to understand.
(Fitzgerald, The Great Gatsby, mrbye.com)

Her upbringing is opposed to the work that has created wealth instead of inheriting it, and she cannot see past her prejudices to understand how similar the two Eggs really are. Gatsby, who fast becomes a star citizen for his parties, is a symbol of New Money, and he is scorned by the East Egg, even though his behavior is almost identical to their own. What they share is wealth; what they do not share is an inclusionary mindset.