How about a mixed tournament? When two countries compete they play their women's teams against each other in the first half and their men's teams against each other in the second half. Similar alternation for ET if needed and penalties.
I think the advantages would be fresher legs throughout the games, more higher intensity play, women being involved a major global sporting event...oh and I think England might win given they are the only team to have made both sets of semi-finals in the women's and men's competition.