Leadership
They are both generals.
Both the President and a monarch rule over people.
Both were republican
They both lived in Illinois when they were elected President.
Both the president and the mayor are picked my the citizens of the US. Both of them are also in great power.
They both start with 'p'
they were both very popular men, and they both were president.
They are both the wife of a president.
they are both dead
Both are in common usage. The US Constitution uses the hyphen as well as capitalization: the Vice-President . Purists might say the hyphen is needed to avoid confusion with a possible president of vice.
They are both legislative bodies, both have a house and senate.
Obviously, both are Goddesses, but going beyond the obvious, neither are mother Goddesses, both are associated with powers an qualities that are often seen as masculine, both seem paradoxically contradictory combining qualities of love and anger, construction and destruction. Both are independent and very free.