Another thing to consider is the nature of the size of armies that could be fielded in the first place and how they fielded them. 100,000 strong armies are not actually a modern phenomena or unique to the Ottomans, even the ancient Chinese would have multiple warring sates each with armies of 100,000 or more in the field. Europe had the feudal system which made much of it's military strength subject to codes and terms of service that often were not actually that long(sometimes vassals in the HRE would only be expected to fight for a month or even a fortnight a year, good luck fighting a campaign in that time, although they could be held for longer but they would have to be paid for it) and the rest was made up of predominately professional or at least semi-professional 'mercenaries'. So all in all the army was decentralised and expensive.

So when looking at the hundred years war, when France massed a force as large as it could to defeat England it was still only 20,000-30,000 strong for a population of 15-20 million or so and on top of that they were hiring mercenaries from Genoa. European armies were often smaller but more professional and better equipped and I think that goes some way to explain why they often failed when launching large expeditions or far flung expeditions. They didn't have the expertise so diesese or malaria would often cripple the army if it tried to leave Europe(as happened to various Spanish and French invasions of North Africa) or even if they managed to reach the foe in a relatively good condition the chain of command was muddled and confused so you end up with the French taking of by themselves to charge head long up the hill against the Ottomans into their trap, ignoring everybody else.