@lowmagekage: I think Tyler Durden is much more intelligent than Travis Bickle and very capable of turning the fight around through improvisation and exploitation of his advantage in versatility but Travis is definitely superior in both physical strength and skill in using either guns of his punches. Tyler lost a fight with Bob and Travis has shown that he could take down ten guys like Bob by defeating an entire small mob involved in prostitution. Travis is also defined by his insanity and rebellious beliefs which are similar to Tyler's so Tyler could not surprise him as easily as he did to anyone else so it's definitely a hard fight as Tyler is too unpredictable for anyone without superpowers to take a victory against him for granted. But Tyler refused to use firearms or kill people so Travis can shoot him and easily defeat him with gunfire although Tyler could hide, use whatever weapons from the environment and dodge bullets while he has shown extreme tolerance to pain and even enjoys it to a degree that it seemingly makes him somewhat stronger. Therefore Travis may be inclined to fight from a distance where he completely overpowers Tyler but Tyler could find an opportunity to ambush Travis and get the upper hand, weakening Travis so that it's not certain if he's manage to retaliate and evenly beat Tyler in hand to hand combat before he's too weakened to continue fighting.
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