I disagree, there is a lot of evidence that the quality of the relationship depends largely on the degree that the man has higher status (overall attractiveness).

To clarify the 'degree' relationship I should add that the relationship is not linear. The optimal status for the man to have is slightly higher but not too much. In fact, when the perceptions of status gap between the partners is too great the guy is well served by raising the girl's status or slightly lowering his own. People get insecure when they think they have no bargaining power at all, insecurity is dangerous.