Adding my five cents to what John 7755 said about martial cultures and conquered peoples: the same applies to conquerors.
A key difference between the Byzantines post 1204 and the Ottomans is that the latter had something called Ghazi culture, which gave them a lot more momentum than the Romans. Turkish Anatolia was much less urbanized than Roman Anatolia way almost until the late 19th century, greatly because the turkic folks that rolled in after Manzinkert preferred to keep a nomadic or seminomadic lifestyle that mirrored as much as possible how it was in Central Asia. An integral part of it was their Ghazi warrior culture: turkic nomadic folk, just like the early arabs, shared a passion (or need depending on the perspective) for raiding and plundering. Islam was born within that context and fit their lifestyle almost perfectly. Being a succesful Ghazi carried huge social status for those guys and brought anlot of prosperiry to their communities in the form of plunder and slaves.
The
Ottomans love for the institution of
ghazw reaches back to the beginnings of their state:
By early Ottoman times it had become a title of honor and a claim to leadership. In an inscription of 1337 [concerning the building of the
Bursa mosque],
Orhan, second ruler of the Ottoman line, describes himself as "Sultan, son of the Sultan of the Gazis, Gazi son of Gazi… frontier lord of the horizons." The Ottoman poet Ahmedi, writing ca. 1402, defines
gazis as "the instruments of
God's religion, a servant of God who cleanses the earth from the filth of
polytheism." (Lewis,
The Political Language of Islam, pp. 147–148, note 8)
This meant that almost every muslim turkish male, regardless of social status, had both the means (a horse, bows, weapons) and the motivation (religion/culture) to risk his life and take part in raids that eventually grew up to become all out conquests. The Sultans almost always had huge armies at their dispossal because most of the young men of their vassal tribes were capable to go on campaign without having to worry about any farms "back home", since they were either nomads or seminomads. In the case they weren't nomads, many still enlisted as azaps, dudes who lived on cities yet were almost always ready to jump on whatever raid or campaign the sultan was planning, living mainly on the plunder they got.
Ever wondered how Bayezid was able to field 85 000 men(almost as much as the Romans in Cannae) in Ankara when not even Justinian or Basil the ll could go beyond 40000 in the heyday of the Byzantine era? There's your answer. Add more political stability and you get the powerhouse the Ottomans were.
Unless the Byzantines were able to somehow replicate a similar, equivalent warrior culture either through a kind of Conquistador or Crusader on roids Spirit+a different kind of Theme system that used more slaves to free the small land owners to equip themselves and train to be soldiers a la Spartans and Helots system, I don't see how they could compare.
Not sure if the Ottomans were significantly more tolerant to Christians than the Byzantines were to Muslims post Macedonian Renaissance or even pre Yarmouk if Heraclius got the tolerance reforms he tried to implement IOTL. The Sultans of Constantinople were no friends of Shi'a muslims and committed their fair share of atrocities to pagan black africans. The life of Christians under thwir rule was not rosy either sfter a while. Feel free to correct me.