The first Crusade was barely more than 30 years after Hastings, and so the armour changed very little. Faceplates developed towards the end of the twelfth century, with protection for the back of the neck coming in during the first quarter of the thirteenth century. It probably wasn't until the ninth Crusade that full fledged great helms were seen in the Holy Lands.

Regarding armour, there would have been no change. Maybe there was a slightly higher proportion of mail chausses, but mail was still expensive enough to make them rare. Even during the ninth Crusade, in 1250, mail was still the main form of armour, as John de Joinville relates in his account of the Crusade. Leather and metal reinforcememts to mail, usually for the arms or legs, appear towards the end of the 13th century and develop from there.

Weapons, too, changed not at all. The primary weapon for a knight was his lance, with a sword and/or some other weapon, like an axe, as their sidearm. Infantry would have been armed with spear and shield, with crossbowmen among their number. Again, even in 1250, the primary weapons of a knight had changed little.

Finally, practical two handed swords are very much a development of the late 15th and early 16th centuries.