Doing something I have not done in a very long while, Monarch lists by equal primogeniture.
Prussia
Frederick I (Hohenzollern) 1713-1740
Friedrike I (Hohenzollern) 1740-1758
Elisabeth I (Hohenzollern) 1758-1780
Frederick II (Hohenzollern) 1780-1786
Alexander I (Hohenzollern) 1780-1806
Charles I (Brunswick-Bevern) 1806-1806
Caroline I (Brunswick-Bevern) 1806-1821 (OTL's Queen Caroline of Great Britain)
Karl I (Saxe-Weimar-Eisenach) 1821-1828
Charles II (Saxe-Weimar-Eisenach) 1828-1853
Marie I (Saxe-Weimar-Eisenach) 1853-1877
Frederick III (Hohenzollern) 1877-1885
Marie II (Hohenzollern) 1885-1888
Elisabeth II (Hohenzollern) 1888-1895
Sophia I (Holstein-Gottorp) 1895-1964
Margaretha I (Bernadotte) 1964-
Netherlands
William IV (Orange-Nassau) 1747-1751
Carolina I (Orange-Nassau) 1751-1787
Frederick I (Nassau-Welburg) 1787-1816
William V (Nassau-Welburg) 1816-1839
Therese I (Nassau-Welburg) 1839-1871
Alexandra I (Holstein-Gottorp) 1871-1900
Nicholas I (Holstein-Gottorp-Romanov) 1900-1929
Nicholas II (Holstein-Gottorp-Romanov) 1929-1931
Marina I (Holstein-Gottorp-Romanov) 1931-1981
Nadejda I (Holstein-Gottorp-Romanov) 1981-1988
Irina I (Holstein-Gottorp-Romanov) 1988-1989
Elizabeth I (Waldstatten) 1989-
Sweden
Charles XI (Palatinate-Zweibrücken) 1660-1697
Hedvig I (Palatinate-Zweibrücken) 1697-1708
Charles XII (Schleswig-Holstein-Gottorp) 1708-1739
Peter I (Holstein-Gottorp-Romanov) 1739-1762
Paul I (Holstein-Gottorp-Romanov) 1762-1801
Alexander I (Holstein-Gottorp-Romanov) 1801-1825
Konstantin I (Holstein-Gottorp-Romanov) 1825-1831
Maria I (Holstein-Gottorp-Romanov) 1831-1859
Marie II (Saxe-Weimar-Eisenach) 1859-1877 (At this point it becomes the Prussia list, eventually concluding with Margaretha, who is of course, Swedish)
I don't think I can make any conclusion after this other than the Holstein-Gottorp's control the world.
Prussia
Frederick I (Hohenzollern) 1713-1740
Friedrike I (Hohenzollern) 1740-1758
Elisabeth I (Hohenzollern) 1758-1780
Frederick II (Hohenzollern) 1780-1786
Alexander I (Hohenzollern) 1780-1806
Charles I (Brunswick-Bevern) 1806-1806
Caroline I (Brunswick-Bevern) 1806-1821 (OTL's Queen Caroline of Great Britain)
Karl I (Saxe-Weimar-Eisenach) 1821-1828
Charles II (Saxe-Weimar-Eisenach) 1828-1853
Marie I (Saxe-Weimar-Eisenach) 1853-1877
Frederick III (Hohenzollern) 1877-1885
Marie II (Hohenzollern) 1885-1888
Elisabeth II (Hohenzollern) 1888-1895
Sophia I (Holstein-Gottorp) 1895-1964
Margaretha I (Bernadotte) 1964-
Netherlands
William IV (Orange-Nassau) 1747-1751
Carolina I (Orange-Nassau) 1751-1787
Frederick I (Nassau-Welburg) 1787-1816
William V (Nassau-Welburg) 1816-1839
Therese I (Nassau-Welburg) 1839-1871
Alexandra I (Holstein-Gottorp) 1871-1900
Nicholas I (Holstein-Gottorp-Romanov) 1900-1929
Nicholas II (Holstein-Gottorp-Romanov) 1929-1931
Marina I (Holstein-Gottorp-Romanov) 1931-1981
Nadejda I (Holstein-Gottorp-Romanov) 1981-1988
Irina I (Holstein-Gottorp-Romanov) 1988-1989
Elizabeth I (Waldstatten) 1989-
Sweden
Charles XI (Palatinate-Zweibrücken) 1660-1697
Hedvig I (Palatinate-Zweibrücken) 1697-1708
Charles XII (Schleswig-Holstein-Gottorp) 1708-1739
Peter I (Holstein-Gottorp-Romanov) 1739-1762
Paul I (Holstein-Gottorp-Romanov) 1762-1801
Alexander I (Holstein-Gottorp-Romanov) 1801-1825
Konstantin I (Holstein-Gottorp-Romanov) 1825-1831
Maria I (Holstein-Gottorp-Romanov) 1831-1859
Marie II (Saxe-Weimar-Eisenach) 1859-1877 (At this point it becomes the Prussia list, eventually concluding with Margaretha, who is of course, Swedish)
I don't think I can make any conclusion after this other than the Holstein-Gottorp's control the world.