At least as far as the Crusades in Syria, Palestine, and Egypt (1st Crusade to the loss of Acre), the armour used by the Crusaders and Saracens was similar. The common armour for armoured soldiers was mail, helmet, and shield. There were differences in detail - Crusader helmets and Saracen helmets differed in style, and Saracen shields were usually round - but the armour provided similar protection.

Armour wasn't static over this period. In the beginning, helmets might be simple conical helmets with a nasal, with more protective helmets appearing during the crusades, such as great helms with full face protection. While Saracen helmets didn't have such complete face protection, cheek pieces and broad nasals gave good protection, much more than earlier helmets with simple nasals. In additional to mail, both sides used textile armour, in combination with mail or as standalone armour. Other metal armour might be worn to reinforce the mail, such as coats of plates (Crusaders) or lamellar armour (Saracens) or scale armour (both).

The armour in use by both sides was similar enough that better quality armour was not a factor in Crusader victories (or losses).

However, neither had had armies composed completely of fully armoured soldiers, and the fraction being armoured cavalry was lower. Armour can make a real difference in Medieval warfare - armoured infantry can withstand a rain of arrows for much longer than unarmoured infantry, armoured infantry and cavalry can overwhelm an equal number of their unarmoured counterparts (if they can catch them!), etc. Numbers given in the sources for the sizes of armies are unreliable, and often no numbers are given for how many armoured soldiers were present. Therefore, it isn't usually possible to tell whether one side outnumbered the other in terms of armoured soldiers. It's possible that some battles went one way or another due to one side having more armoured soldiers, but we can't tell if this was the case.

Notably, the Saracen states were very divided, busy fighting each other, and underestimated the Crusader threat during the First Crusade, and often sought to exploit the Crusaders for their own gain in their local power struggles. This certainly contributed far, far more to the success of the First Crusade than any possible superiority in armour or in the number of armoured soldiers. After the First Crusade, the Crusaders were generally less successful, and lost in the long run. The major change was that the Saracen states were less divided, and the Crusader states more divided than during the First Crusade. (Indeed, it wasn't that long after the First Crusade when we see major battles with both sides consisting of Saracen and Crusader allies.)