It is when it comes to financial independence that very often--but not always--male and female characters want different things from marriage in Persuasion. It is true that female characters like Anne, Elizabeth, and Louisa want marriage to a man with a reasonable fortune so they can live within the standards of their social class(es). Yet it is also true that men like cousin William Elliot--who either have no independent fortune or have squandered their fortunes away--also put consideration of the wealth of the lady in a high position of importance, sometimes in the first position of importance. (Colonel Fitzwilliam of Pride and Prejudice is an example of the first sort of man, one without fortune.)
The greatest difference between what female and male characters want from marriage is independence. If female characters don't have independent fortunes, they must marry, and marry well, if they are to be independence--although independence can be attained by an unmarried woman if she also accepts poverty and a lowering of social class, a condition few female characters are willing to accept. Mrs. Smith represents this condition of independence.
On the other hand, men have independence from the age of majority (21) onward, even if they have not got independent fortunes. This is because they have full opportunity for education and careers, though their family's wealth and social position can restrict the range of both. Independence represents the greatest difference between what the male and female characters want out of marriage.