Gilgamesh is nerfed by plot. He wins. I don't know about badass though. Both are awesome but I don't know why I don't like archer that much. Some aspects are awesome and the whole unlimited blade works spell is epic but not fond of the character. Gilgamesh on the other hand is just well, Gilgamesh.
PS-Filthy mongrels can't compare to the king of heroes.
Who has a wider arsenal? I don't know. Both have a wide variety of weapons but Archer has unlimited weapons and Gilgamesh has a limited amount but it is much more powerful.
Who'll win in a fight? Gilgamesh. Archer's only chance of winning would be to take him out before he pulls out Ea.
Gilgamesh is the strongest servant. Although archer is one of those servants who have a chance of defeating gilgamesh IF Gil fought like he always does.