Both are betrayed by their party leader after wanting to become foreign secretary (secretary of state American equivalent)
Both of them take their revenge.
Underwood might be derived from the name Urquhart which is "variously translated from the Gaelic, including 'woodside', or 'by a rowan wood', or 'fort on a knoll' ("Scottish Clan & Family Encyclopedia" by George Way, 1998)
Both "break the fourth wall" by talking direct to the viewing audience through the camera.
They both have an assassination attempt on them.
Different second name (though may be derivative, see similarities).
Urquhart is from a very privileged family, while Underwood had to work his way up.
Underwood survives the assassination attempt, while Urquhart does not.