Dexter is "newer and stronger" in that he is the son of an immigrant mother and a member of the working class by birth. He is not a child of privilege; his family is not one that has built and inherited wealth for several American generations. Dexter worked from the time he was a boy because he needed the money, and he worked hard to attend a fine Eastern university, instead of settling for the less expensive state university. Going to a prestigious school was not a birthright for Dexter as it had been for the sons of the wealthy. After college, Dexter continues to work hard, building a business from very little except his own ingenuity. As a result, he becomes a quite wealthy young man. He is strong in that he knows how to work and plan for what he wants in life.
Dexter is superior in numerous ways to the idle rich he had grown up admiring; ironically, however, he wants his children to be children of social privilege. Dexter wants them to enjoy what he perceives to be the beauty, glamour, and romance of upper-class wealth.
Dexter Green is "newer" than the "careless" wealthy people since wealth has been unfamiliar to him and not a matter of course. He also is "new" in the sense of being somewhat naive about what wealth can really bring him.
Dexter is "stronger" because for him wealth is itself a means to a goal, but he is confident that he can attain it. On the other hand, the "careless" rich take their wealth and all that it affords them for granted. They feel no powerful need or deprivation. Once he attains his wealth through hard work and confidence, Dexter values this wealth as something that he must protect because he knows that without it, he cannot attain his goals. The "careless" wealthy often do not sense a real danger as Dexter does.
After Dexter has met the wealthy Judy Jones, who is "arrestingly beautiful," he sets his sights on becoming one of her social and economic class. Thus, he is driven to attain wealth: "...he wanted the glittering things themselves." Moreover, he is "unconsciously dictated by his winter dreams" of becoming rich. In his confidence Dexter chooses to attend a prestigious Eastern college over a state school. Eventually, he becomes a success in his own business.
But all that Dexter accomplishes is not done for the attainment of money per se. He desires wealth for a stronger purpose: the attainment of his dream of a perfect life that involves Judy Jones and her love.