The answer to this question relevant to Persuasion is as subjective as it is to contemporary males and females. People want various things from marriage depending upon their values, moral character, ambitions, social position, and dreams for the future. Having said that, it is possible to surmise some of the marital motives and aspirations for at least some of the characters in Persuasion.
Starting with Sir Walter Elliot and Lady Russell, they want very much the same out of marriage, although circumstances nearly sway Sir Walter's opinions as a result of Mrs. Clay designs. Sir Walter and Lady Russell both require marriage to provide proper social prestige, advancement, and financial security. Hence, individuals who applied for Elizabeth's hand were more often than not deemed undesirable. Cousin William and Elizabeth share their opinions. As a result of Elizabeth's opinion, she rejects years' worth of suitors until she is on the outer fringe of the social circle of wealth, prestige, and youth, leaving her with the distinct possibility of continued spinsterhood. So in these regards, these male and female characters want the same things out of marriage on these points.
Anne and Wentworth have different opinions from the above characters on what is wanted out of marriage. Anne and Wentworth both want to be wed to someone whom they truly love, whether the other is with or without a fortune. Of course they are both practical enough to realize that there must be strong future prospects for income, which Wentworth had when he courted Anne, although Lady Russell and Sir Walter rejected the plausibility of his prospects. In addition, as the window and letter scenes tells us, both Anne and Wentworth want constancy of feeling and devotion. Again, both male and female want the same thing.