The military Orders on the whole were pretty disciplined and professional bunches by the standards of the time, and that made them considerably better fighters than most normal knights. The fact that they were also prone to be religious zealots didn't hurt.

Anyway, they naturally fought in the best armour of the time they could get. I'll bet the habit of wearing robes or surcoats over the armour was there from the start - there's good practical reasons to cover metal worn from the merciless Mediterranean sun after all, and all "Franks" in the Outremer wasted no time copying the local practice of doing so.

Although I thought the Templars' colours were red on white...? You'd think that was used on most shield blazons too... And respectively the Johannites/Hospitallers has white on black and the Teutonics black on white, IIRC - the numerous smaller Orders I know rather less about.