Yes, your premise is correct. However, the rich have more concerns and worries than the poor. Not to mention an entirely different set of needs/wants. All people are the same, its just different perspectives.
More? Perhaps. More pressing? That's debatable. The poor worry about the cost of groceries, the cost of their children's education, the cost of medical care, and retiring with dignity and basic comforts like shelter and utilities. By definition, the poor are living on the edge, with the ever present possibility of falling short of life's most basic needs. You know, survival. While the rich don't concern themselves with such base trivialities, they must turn their attention to the latest fashion trends, being invited to the right parties and making X multiples of all the money they will ever need to live their lives in whatever manner they choose. You know, "self-actualizing." Perhaps the rich have more worries because they have more choices. If you try not to make light of the worries of the poor, I'll try not to make light of the worries of the rich.