What differences in costume and equipment were there between the armies of the Islamic conquest and those of the Crusades (Saracens)?
In Conquest armies you would find a mixture of Desert Arabs (Bedouin) and Roman style Arabs/ Persian style Arabs. The latter types wore costumes akin to those of the Hatrans and Palmyrenes that you might call Syrian. I think we are talking longish long sleeved tunics and baggy trousers, Doubtless Arabs in Iraq looked a bit more Persian, though it would be somewhat like Syria. The Desert Arabs are described as semi naked and probably looked like the figure on the chair of Bishop Maximian who is wearing a long piece of cloth wrapped around him. We can be fairly certain this is accurate because an Arab emissary to the Persian court is described as unclad and creates a colourful tabard for himself by cutting a slit in an expensive carpet and putting his head through it!
I would think the Bedouin types generally lacked armour, but the town Arabs definitely had long coats of mail or scale and round helmets. They likely also wore elements of Persian and Roman armour, especially after the early victories.
I don't think turbans were universal, if used at all until contact with India. Rather the Arabs wore a cloth that went over the head and wrapped like a scarf.