When were they the most powerful empire in Europe?

The Ottoman Empire, during the 1500s and most of the 1600s, was one of the strongest empires in Europe. Conquests of southern Europe and the middle east, along with various tribute states in the Caucasus and north Africa gave them a position of power that concerned Central and Eastern Europe. Many would mark the end of Ottoman power at the siege of Vienna in 1683, in which Poland Lithuania, Austria, and other German states crushed an ottoman army, pushing the Ottomans out of most of modern day Hungary, Transylvania, and Croatia.

In the 1700s, Austria and Russia would continue to chip away at the Ottoman empire and its vassals, while the empire internally reformed. By the end of the Napoleonic era, nationalist movements, supported mostly by Russia, further splintered the empire. And with the independence of Greece, it was obvious the Ottomans were no longer a power to negotiate with, but to negotiate over. This was a further issue as the centuries old aristocracy was displeased with modernization, as it would undermine their own authority.

While it is difficult to say who replaced the Ottomans as the dominant power in Europe, the Austrian and Russian empires by 1914 had the upper hand in the Balkans, while British support of Arab independence threatened the territories in the middle east.