The Ottomans...for a short time....held the military advantage in Eastern Europe...but their sophistication, as you call it...was nothing more than their "acquisition" of Byzantine culture, dressed up in their Ottoman custumes.....The Ottomans in no way challenged the supremacy of Spain...that would be left to the English barbarians....and their infernal "pirates" such as Francis Drake...
First off, you are naively mistaken in ascribing all possible "sophistication" to mere looting of an already ruined civilization: only the educational and hygienic system of the empire, evident in the mosque complexes and the system of baths that had disappeared centuries before in the Greek Empire, were their own work, not something acquired. Even the actually false pretense, so often repeated in old Western historiography, which considered the Greek Empire as having just acquired a capital inherited from classical Greek and Romans, and which they would have progressively wasted without adding anything of their own, for all its being false, is much closer to what you say about the Turks.
Then, I was not talking about the Turks challenging the supremacy of Spain IN THE WEST, which has always a private coop for Western European nations, but referring to their respective positions as a global power, and that in terms of their general development, and more as a whole civilization than as a military power. But even from the military perspective, just like the Spanish might was not over after the Armada disaster (go tell the Dutch, in particular), in Lepanto the Turkish were not actually bent by the Spanish. Cheap national pride and propaganda can present things as they please, but any historiographical effort minimally aspiring to accuracy must always bear into account that there is a capital difference between surpassing (punctually) and bending... and, of course, smashing. It has happened the same with the American in Vietnam or even Somalia... although Somalia is more like Afghanistan: nobody, from Alexander to the British and the [STRIKE]Soviet[/STRIKE] Russians, could ever aspire to impose anything, let alone military, in a territory like that, were armies do not fight armies and not even "elements", but the ghost of a war spirit, more agile and deadly than Spanish guerrillas. And please, Drake and piracy in general were just mosquitoes: the bigger problem of Spain has always been Spain herself.
I wasn't extolling their nature, I was pointing merely to the fact that the higher place and power was theirs... faute de mieux, for over one century: just like with the case of Spain. The fact that they became progressively irrelevant after the mid-XVIIth century is greater proof that they were not solid powers.
Even accounting for the brief period in which all powers indisputably held sway over the rest, both the Spanish and Turkish empire were propped more by mere military strength than by a political and economic system that has given Britain one more century of brilliant decadence. In the case of Spain, more than a true economic system, is te huge stash of wealth from the American colonies what availed them of the resources to remain, not so much a relatively relevant power, which they were actually not, as a pure presence in the political board until the early 1800s.
So your post was basically a string of old-fashioned, "acquired" [pseudo]historiographical commonplaces and inaccuracies one after the other.