What if the Ottoman Empire didn't fall apart in the period 1586 to 1599?
Since it subsequently, well, Ottomanized* into more than a dozen nations, which were preyed on by outside powers, I'd think there would be a big difference. Maybe the 'Turkish Caliphate' would continue to prosper.
Also one has to wonder what continued Islamic rule would be like in the Balkans. Some areas already had Turks living in them and had many converted Slavs, so if the Ottomans survived for a few more centuries those areas might become fully Muslim.
I wonder if that would lead to connection with the rest of the surviving Ottoman Empire and thus prosperity, or if maybe centuries on, the Christians and Muslims in the Balkans would fight amongst eachother and cause the region to Ottomanize.
Surely the Balkans would be much different than the peaceful, very Catholic (and Orthodox in Bulgaria's case), 'traditionalist'-but-modernizing land they are today that's reminiscent of some of the Italian nations to the west.
* (OOC: fractured or Balkanized)