Why did the Turks in the 14-15th centuries usually have military superiority over Christians?

Well, consider the example of the Christian capital of Byzantium, which later became Istanbul – the center of those very Turks.
Against the backdrop of a strong Ottoman Empire, such Byzantines, Serbs, etc. were quite weak. The Turkish army was not inferior in organization and fighting qualities + numerical superiority. Most often in battles, the latter played a major role. The Turks also had an excellent strengthening of the central government, and the sultans themselves believed that the strengthening and unity of the state played a vital role. With their help, the ruler kept the people of the conquered country in check.
In general, in those days the Ottoman Turks were the most powerful warriors that existed at all. It is not surprising that they drove out Christians and not only.