The "templers" were not defeated, the first crusades result was nothing short of absolute dominance over armies many times their own size. Denying that mail+aketon had a huge deal to do with that is a rare display of ignorance.
Most of the armies the crusaders faced in the first crusade were equipped almost identically to west european armies but with contingents of horse archers. Their lancers were mailed, and the spear infantry that made up the core of their armies wore padded mail. If anything, from the start of the crusades to about 1200 the muslims had access to better armour.
Also the crusades in general are a long string of defeats where the various muslim states just didn't have the impetus or motivation to finish them off by sieging their castles.