Ottoman persistence and eventual success in attacking Constantinopole had everything to do with their imperial priorites and skill in siege warfare and preciously little to do with religion. And they had to try several times, too. And it was *still* a pretty close run thing.

Back in the 7th century or so the Arabs had besieged the place for years, to no avail (I think the Emperor eventually managed to offer them enough tribute to get them call it off). And they were still running on the high gear of the newly established faith's militant expansionism phase. The as-such usefully unifying religious fervor didn't much keep them from having serious issues with Sassanid war elephants, however, and routing from several battles for other reasons. Ditto for the Moors when they butted their heads bloody against Frankish lines at Poitiers, 732 AD.

Conversely, firm belief in a direct ticket to Heaven through martyrdom did not to my knowledge make either crusading European armies or the military Orders in some way unbreakable. Some of course were; but when the push really came to shove, most would panic and run like any other soldiers in the same situation.

The Muslim (initially really Arab) ability to overrun a poerful, long established empire and bring another to its knees in their initial Blitzkrieg came from many reasons, but among the chief ones was the simple fact Byzantium and the Sassanids had been fighting each other more or less intensively for quite a while and were caught in a rather weakened state. The Arabs may not have been steppe nomads, but quite a few of them were desert nomads and hence capable of considerable strategic mobility, especially in deserts, that the imperial armies found difficult to match.

Around those times pikes had fallen from use (although to my knowledge standard one-handed infantry fighting spears the world over have tended to reach lenghts of some two and half meters that doesn't quite compare to the up to 5.5 meter Hellenic and Medieval pike...) anyway, and the Arabs swiftly copied the cataphract principle to the extent their resources allowed - which in practice meant most of the horses had to make do with hardened leather barding, for example. Well, at least that kept the load down and retained greater mobility.