How about "A Hymn to Him" and "An Ordinary Man" from MY FAIR LADY?
Also, I'm not that familiar with the show, but I'm sure THE LAST FIVE YEARS has a song or several about men and/vs. women.
Salve, Regina, Mater misericordiae
Vita, dulcedo, et spes nostra
Salve, Salve Regina
Ad te clamamus exsules filii Eva
Ad te suspiramus, gementes et flentes
O clemens O pia