The Ottomans were actually ruled by a sultan while kings rule the Persians. The Ottomans were basically followers of Islam, while the Persians were believers of Zoroastrianism. Though the two empires were very powerful during their time, the Ottomans ruled for well over 600 years while the Persians reigned for a little more than 200 years.
What led to the downfall of the then Ottoman Empire was corruption and poor leadership while the Persian Empire fell because Alexander the Great of the nation of Macedonia defeated the Persian army when they met in several battles.
The major Ottoman legacy to the world includes the spread of Islam, major architectural wonders, and artistic pursuits while the Persians are credited for creating the foundations of the postal system, allowing autonomy for different ethnicities, the use of road networks, the adoption of just one single language for administration and also the practice of bureaucracy.