At first glance, common sense would seem to dictate that a patriot (given both their superior human intelligence and superior firepower) would have the clear edge. HOWEVER, this fails to give due credit to the Falcon's razor sharp claws, breakneck air speed and super enhanced vision. This third point is the true leveling factor: while the Falcon will recognize his enemy immediately, the patriot may hesitate to shoot a far off spot in the sky (fearing he may accidentally target a bald eagle- the favored bird of his people).
Still, the Patriot has the ordinance needed to take his foe out at a distance. If he doesn't underestimate the wily cunning of nature's fastest predator, or himself to be blinded by love of country (or the cruel beak of a falcon) his march to victory should be secure.