In terms of military technology, the Crusaders and Muslims were on a roughly equal footing with each having advantages in certain areas. Terrain and weather could also matter enormously to the success or failure of particular tactics or weapons.

The Muslims preferred hit and run tactics practised by light archers, often on horseback. This had been a pretty standard strategy since the days of the Parthians, and the fundamental idea of hit and run assaults with mounted archers was still the backbone of ranged infantry tactics during the earlier crusades. However, by the First Crusade advances in European armour meant that these tactics just weren't good enough. The First Crusade encountered this tactic at the Battle of Dorylaeum, where it was observed that the bows of the Turks lacked the power to penetrate the mail armour of the crusaders. The crusaders were able to simply stand with their shields for hours on end, and then charge once the Turks ran out of arrows. By the Third Crusade, the bows typically used by Muslim soldiers weren't much better. Multiple sources compare the crusaders at the Battle of Arsuf to hedgehogs, because they had so many arrows sticking out of them yet remained unharmed. This is not to say their bows were useless - lesser equipped infantry were vulnerable, and as the Gesta Francorum - our main source for the First Crusade - noted, it was only a matter of time until an arrow found some gap in a knight's armour.

However, this doesn't mean that Muslim archery was technologically or strategically primitive. It's worth noting that the Muslims of the Near East were fully capable of making very powerful bows, but they were expensive and difficult to maintain. This was a problem when nearing the humid coastline, which had a tendency to weaken the glue used in the bows and render them severely weakened. This caused particular frustration to Baha ad-Din, a close associate of Saladin who expressed dismay at the sudden weakness of Muslim archers at Arsuf, and the apparent strength of the crusader archers and crossbowmen by comparison. The Muslims had developed a tried and tested strategy that should have worked. In essence, the idea was to provoke their enemy with the light archers, at which point the crusaders would charge at them. The archers, being on horseback, would then fall back rapidly. The flanks of a Muslim army - often sturdier infantry and heavier horsemen - would stay put. You can probably see the trap. The flanks would then close in and inflict a crushing defeat, like Hannibal at the Battle of Cannae. It had worked many times, and the cultural importance of appearing brave and valiant by charging the enemy among Europeans meant that it kept working. The problem at the Battle of Arsuf was that Richard the Lionheart was well aware of what Saladin was trying, and did his best to keep his men moving in the knowledge that their armour could take the blows - Richard's plan only failed when the Knights Hospitaller, and then a group of French knights, broke ranks and charged because they were impatient. At that point he peeled away the crusader marching column into one giant blob of heavy cavalry heading straight for Saladin's banner - it was crude but effective, and Saladin was forced to flee and regroup.

The Battle of Arsuf, and subsequent Battle of Jaffa, exposed the strengths of European archers, especially the English. Richard had brought contingents of longbowmen and crossbowmen numbering 2000 men, and they tore through Saladin's light horsemen in devastating barrages. When Saladin ordered an all out charge at the Battle of Jaffa, not one horse made it to Richard's lines. The longbows were used to slow the enemy down, whilst the crossbows picked off Saladin's horsemen one by one. After one particularly bad charge, Richard got onto his horse and openly galloped in front of the Muslim line taunting them about their losses.

In siege technology the two sides were roughly the same, though the Muslims did have one significant advantage. Both sides preferred to apply pressure to surrender by demolishing fortifications with trebuchets and sapping. Quite often the mere sight of a siege tower rising, or a wall collapsing due to sapping, was enough to provoke the opening of negotiations. The crusaders were certainly more predisposed to a violent end to sieges, the allure of glory by going over the walls was too much for a lot of knights, but the norm was nevertheless to negotiate rather than take a city by storming it.

The advantage of the Muslims, however, was in incendiary weapons. The Crusades feature a few instances of the Franks using flaming ballista bolts and other primitive incendiary weapons to try and ignite enemy siege engines, but the Muslims were experts in the deployment of naphtha based weapons. These were often as simple as some oil in a jar with a fuse sticking out of it, but it was more than the crusaders had because the Crusader States were not exactly oil fields, and lacked the knowledge of how to distil crude oil efficiently. At the Siege of Acre, the crusaders had constructed three enormous siege towers, each large enough to have a trebuchet built on the top of them to fire into the city. The city was considering surrender, but a Muslim happened to arrive at Saladin's camp asking to be smuggled into the city, claiming to have a new recipe for an incendiary bomb that he called 'white naphtha'. We aren't sure exactly what the man's concoction was - though it seems to have been a form of what we'd now call white spirit or petroleum spirit - and it burned all three towers to the ground in minutes after exploding in a mighty fireball on impact. The crusaders had nothing that could compete with this, and the substance almost instantly reversed the momentum of the siege until Richard arrived with his array of siege engines. Saladin is said to have offered the man titles and land for his achievement, but he refused saying that he worked only for God, and would only be rewarded by God.

So there were some ways in which the Muslim armies were superior. They had more developed tactics based on extremely sound strategy, but were let down by the insufficiency of their bows in comparison to European armour, and in a simple slogging match the archers of the crusaders could win with ease. They used the same siege tactics as the crusaders, but had the additional benefit of naphtha incendiary devices. Often the crusaders could overcome this by covering their siege towers in wet hides, but not always.