Well, first of all that's depend on the period, the knights of those orders followed the technology of the time, so it was first mail, than after that reinforced with plate, beginning in the late 13th (coat of plates, for exemple), than a shift, during the 14th, to plate armour (limbs protection, like greaves), in the late 14th, early 15th, you pretty much have full plate armour, with mail under it (sleeves and skirts, or even a full shirt).

The equipment could varies, regionally, for exemple the Teutonic knights have some "Prussian shields" in their inventories and accounts

You need to keep in mind, however, that the Templars went down early in the 14th.

Sources: CAPWELL Tobias, Armour of the English Knight 1400-1450. BAPTISTE Nicolas, Armatus Corpus, Princes et Chevaliers (1330-1530). NOWAKOSKI Andrzej; Arms and Armour in the Medieval Teutonic Order’s State of Prussia