I talked to two american persons. And firstly, they said "The Dream of Home Ownership" is better.
And about the Marcio's question, they said "The Dream of owning a car".
I asked them if "The Dream of Car Ownership" is correct, they said that you could and it would make sense. But unless it was used in the right context it would sound odd, and it is perfectly understandable, but it has to be used correctly as part of a larger sentence.
I hope I have helped.